Method Reducible to Equations separable Homogeneous
Chapter 2 Homogeneous Differential Equation Homogenous Differential Equations A differential equation Homogenous differential equation if every t, where t R Chapter 2 2
Chapter 2 Homogeneous Differential Equation Example: 1. Show that differential equation is homogenous differential equation. Solution: Differential equation is homogeneous Chapter 2 3
Homogeneous Differential Equation Chapter 2 METHOD for solving Homogenous differential equations Substitute OR Substitute Chapter 2 4
. Homogeneous Differential Equation Chapter 2 Using substitution the homogeneous differential equation is reduce to separable variable form. Example: 2 Solution: Solve the homogenous differential equation Rewriting in the form : substitute and Chapter 2 5
Chapter 2 Homogeneous Differential Equation is variable separable form is general solution. Chapter 2 6
Chapter 2 Homogeneous Differential Equation Note. Selection of substitution Differential Equation depends on number of terms of coefficients 1. If , then take 2. If , then take 3. If , then take Chapter 2 x = vy or y = ux 7
Solve the Differential Equation by using appropriate substitution (1 / 2) Chapter 2 Example: . Homogeneous Differential Equation Solution: Differential equation is homogeneous as degree of each term is same, hence we can use either y = ux or x = vy as substitution Substituting y and dy in the given equation Chapter 2 8
Homogeneous Differential Equation Chapter 2 Separating variable u and x (2 / 2) is Separable form Integrating both the sides is general solution of the differential equation Chapter 2 9
Example: Show that differential equation (1 / 2) Solution: Homogeneous Differential Equation Chapter 2 is homogeneous Chapter 2 10
Homogeneous Differential Equation Chapter 2 is Separable form (2 / 2) Integrating both the sides Let is general solution of the differential equation Chapter 2 11
Chapter 2 12 Homogeneous Differential Equation Chapter 2
Homogeneous Differential Equation Chapter 2 (1 / 3) Chapter 2 13
Homogeneous Differential Equation Chapter 2 (2 / 3) Chapter 2 14
Homogeneous Differential Equation Chapter 2 (3 / 3) Chapter 2 15
Chapter 2 16 Homogeneous Differential Equation Chapter 2
Homogeneous Differential Equation Chapter 2 (1 / 2) Chapter 2 17
Homogeneous Differential Equation Chapter 2 (2 / 2) is general solution Chapter 2 of differential equation 18
Chapter 2 19 Differential Equation Chapter 2
Chapter 2 20 Differential Equation Chapter 2
Chapter 2 Differential Equation is general solution of differential equation Chapter 2 21
Differential Equation Chapter 2 Example : By Substitution
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