NCERT Solutions for Class 12 – Mathematics – Chapter 9 – Exercise 9.5 – Differential Equations – Homogeneous Differential Equations

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An equation involving the derivative (derivatives) of the dependent variable with respect to the independent variable (variables) is called a differential equation.

The order of a differential equation is defined as the order of the highest order derivative of the dependent variable with respect to the independent variable involved in the given differential equation.

By the degree of a differential equation, when it is a polynomial equation in derivatives, we mean the highest power (positive integral index) of the highest order derivative involved in the given differential equation.

Order and degree (if defined) of a differential equation are always positive integers.

A differential equation is said to be linear if the dependent variable and all of its derivatives occurring in the equation occur only in the first degree and are not multiplied together.

A differential equation will be a non-linear differential equation if

(i) its degree is more than one;

(ii) any of the differential coefficients has exponents more than one;

(iii) products containing dependent variable and its differential coefficients are present.

Solutions of First-Order Linear Differential Equations are given below.

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CBSE    Class 12   NCERT Solutions    Mathematics
 Inverse Trigonometric Functions
Determinants – Chapter 4
Determinants Chapter 4 Exercise 4.1 and 4.2
Determinants Chapter 4 Exercise 4.3 and 4.4
Determinants – Chapter 4 – Exercise 4.5
Determinants – Chapter 4 – Exercise Miscellaneous
Continuity and Differentiability – Chapter 5
Continuity and Differentiability – Chapter 5 – Exercise 5.2
Continuity and Differentiability – Chapter 5 – Exercise 5.3
Continuity and Differentiability – Chapter 5 – Exercise 5.4
Continuity and Differentiability – Chapter 5 – Exercise 5.5
Continuity and Differentiability – Chapter 5 – Exercise 5.6
Continuity and Differentiability – Chapter 5 – Exercise 5.7
Integrals – Chapter 7
Integrals – Chapter 7 – Exercise 7.1
Integrals – Chapter 7 – Exercise 7.2- Integration by substitution
Integrals – Chapter 7 – Exercise 7.3 – Integration using trigonometric identities
Integrals – Chapter 7- Exercise 7.4 – Integrals of Some Particular Functions
Integrals – Chapter 7 – Exercise 7.5 – Integration by Partial Fraction
Integrals – Chapter 7- Exercise 7.6 – Integration by parts
Integrals – Chapter 7 – Exercise 7.7 – Some special types of standard integrals
Integrals – Chapter 7 – Exercise 7.9 – Definite Integrals 
Integrals –Chapter 7 – Exercise 7.10 – Definite Integrals by Substitution
Integrals – Chapter 7 – Exercise 7.11 – Definite Integrals using Properties
Differential Equations –Chapter 9 – Exercise 9.4 – Differential Equations with Variable Separable
Differential Equations – Chapter 9 – Exercise 9.5 – Homogeneous Differential Equations
Differential Equations –Chapter 9 – Exercise 9.6 – First-Order Linear Differential Equations

 

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Differential Equations – Solutions of Homogeneous Differential Equations – NCERT Solutions – Class 12 – Mathematics – Chapter 9 – Exercise 9.5

XII M NCERT Differential Equations 9.5 (1) XII M NCERT Differential Equations 9.5 (2) XII M NCERT Differential Equations 9.5 (3) XII M NCERT Differential Equations 9.5 (4) XII M NCERT Differential Equations 9.5 (5) XII M NCERT Differential Equations 9.5 (6) XII M NCERT Differential Equations 9.5 (7) XII M NCERT Differential Equations 9.5 (8) XII M NCERT Differential Equations 9.5 (9) XII M NCERT Differential Equations 9.5 (10) XII M NCERT Differential Equations 9.5 (11) XII M NCERT Differential Equations 9.5 (12) XII M NCERT Differential Equations 9.5 (13)
CBSE    Class 12   NCERT Solutions    Mathematics
 Inverse Trigonometric Functions
Determinants – Chapter 4
Determinants Chapter 4 Exercise 4.1 and 4.2
Determinants Chapter 4 Exercise 4.3 and 4.4
Determinants – Chapter 4 – Exercise 4.5
Determinants – Chapter 4 – Exercise Miscellaneous
Continuity and Differentiability – Chapter 5
Continuity and Differentiability – Chapter 5 – Exercise 5.2
Continuity and Differentiability – Chapter 5 – Exercise 5.3
Continuity and Differentiability – Chapter 5 – Exercise 5.4
Continuity and Differentiability – Chapter 5 – Exercise 5.5
Continuity and Differentiability – Chapter 5 – Exercise 5.6
Continuity and Differentiability – Chapter 5 – Exercise 5.7
Integrals – Chapter 7
Integrals – Chapter 7 – Exercise 7.1
Integrals – Chapter 7 – Exercise 7.2- Integration by substitution
Integrals – Chapter 7 – Exercise 7.3 – Integration using trigonometric identities
Integrals – Chapter 7- Exercise 7.4 – Integrals of Some Particular Functions
Integrals – Chapter 7 – Exercise 7.5 – Integration by Partial Fraction
Integrals – Chapter 7- Exercise 7.6 – Integration by parts
Integrals – Chapter 7 – Exercise 7.7 – Some special types of standard integrals
Integrals – Chapter 7 – Exercise 7.9 – Definite Integrals 
Integrals –Chapter 7 – Exercise 7.10 – Definite Integrals by Substitution
Integrals – Chapter 7 – Exercise 7.11 – Definite Integrals using Properties
Differential Equations –Chapter 9 – Exercise 9.4 – Differential Equations with Variable Separable
Differential Equations – Chapter 9 – Exercise 9.5 – Homogeneous Differential Equations
Differential Equations –Chapter 9 – Exercise 9.6 – First-Order Linear Differential Equations

 

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             ISC              Class 12                   Mathematics

Previous Years Board Questions Solutions of Previous years Board Questions
Inverse Trigonometric Functions (2000 to Sem 1-2021) Inverse Trigonometric Functions (2000 to Sem 1-2021)
Matrices (2000 to Sem 1 – 2021) Matrices (2000 to Sem 1-2021)
Determinants (2000 to Sem1-2021) Determinants (2000 to Sem1-2021)
Differentiation (2000 to Sem 1- 2021) Differentiation (2000 to Sem 1- 2021)
L’ Hospital’s Rule (2001 to Sem1-2021)
L’ Hospital’s Rule (2001 to Sem1-2021)
Rolle’s Theorem and Lagrange’s Mean Value Theorem (1998 to 2020) Rolle’s Theorem and Lagrange’s Mean Value Theorems (1998 to 2020)
Maxima and Minima (2000 to Sem 1-2021) Maxima and Minima (2000 to Sem 1 – 2021)
Integration (1990 – 2011) Integration (1990 – 2011)
Integration (2012 to 2022) Integration (2012 to 2022)
Differential Equations (1991 to 2005) Differential Equations (1991 to 2005)
Differential Equations (2006 to 2022) Differential Equations (2006 to 2022)
Probability (Addition and Multiplication Theorem-Conditional Probability) (1993 to 2022) Probability (Addition and Multiplication Theorem, Conditional Probability) (1993 to 2022)
Probability (Baye’s Theorem) (2000 to Sem 2-2022) Probability (Baye’s Theorem) (2000 to Sem 2-2022)
Probability (Probability distribution and Binomial distribution) (1992 to 2020) Probability (Probability distribution and Binomial distribution) (1992 to 2020)
Application of Calculus in Commerce and Economics (2005 to Sem 1-2021) Application of Calculus in Commerce and Economics (2005 to Sem 1-2021)
Linear Programming (2008 to Sem 2-2022) Linear Programming (2008 to 2022)
Linear Regression (2005 to 2013)
 Linear Regression – (2005 to 2013)
 Linear Regression (2014 to 2022) Linear Regression –  (2014 to 2022)  
                MCQ              Class 12         Mathematics

Relations and Functions
Inverse Trigonometric Functions
Matrices
Determinants
Continuity and Differentiability
Tangents and Normals
Maxima and Minima
Increasing and Decreasing Functions
Application of Calculus in Commerce and Economics (Set I)
Application of Calculus in Commerce and Economics (Set II)
Integration MCQs (Set 1)
 Integration MCQs (Set 2)
Specimen Paper for Semester 1 – 2021 – ISC – Class XII Mathematics
Linear Regression
ISC   –   Class 12  –  Mathematics  –  Sem 2  –  2022  – Sample Paper

                            Sample Paper 1
                            Sample Paper 2
ISC – Class 12 –  Mathematics – Sem 1 – 2021 – Sample Paper

                         Specimen Paper
ISC- Class 12 – Mathematics – Sem 2 – 2022 – Chapterwise Questions

                      Differential Equations (Set 1)
                      Differential equations (Set 2)
                      Integration
                     Probability
                     Linear Programming (LPP)
ICSE – Class 10  -Mathematics   –     Sem 2  –    2022 – Sample Paper

                              Sample Paper 1                Solutions of Sample Paper 1
ICSE – Class 10 – Mathematics –  Sem 1-  2021 – Sample Paper

Mock Question Paper

 

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                 MCQ               Class 10            Mathematics

Banking (Set 1)
Banking (Set 2)
GST
Linear Inequations (Set 1)
Linear Inequations (Set 2)
Quadratic Equations
Factorization
Ratio and Proportion
Matrices
Arithmetic Progression (A.P.)
Similarity (Set 1)
Similarity (Set 2)
 Reflection
Section Formula
 Straight Lines
 Probability
Circle (Set 1)
Circle (Set 2)
Mock Question Paper for Semester 1 (2021) ICSE Class X Mathematics
ICSE Class X – Specimen Question Paper released by CISCE for Semester 1 (2021) – Mathematics

 

          MCQ         Class 10      Physics

Sound

 

 

            Formula             Mathematics

Formula and Theorems for Class X
Class XI Formula Trigonometry
Inverse Trigonometric Functions – Class 12
 
Differentiation and Limits for Class 11 and 12
 
Integration for Class 11 and 12
 
 Linear Regression – Class 12- ISC

 

     ISC / ICSE  Board Paper

ISC  – Class 12 – 2020 – Mathematics Question Paper
ISC –  Class 12 – 2019 –  Mathematics Question Paper
ISC Class 12 Semester 1- 2021 Mathematics Question Paper with Solution
ISC – Class 12 – Semester 2-2022 Mathematics Question Paper with Solution
ICSE – Class 10 – 2020- Mathematics Question Paper 
ICSE – Class 10 – 2019 – Mathematics Question Paper
ICSE – Class 10 – 2018 – Mathematics Question Paper
ICSE – Class 10 – 2019 – Physics Question Paper
ICSE – Class 10 – 2018 – Physics Question Paper 
ICSE – Class 10 -2020- Mathematics Question PaperSolutions

 

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