Second Order Linear Differential Equations

How do we solve second order differential equations of the form \[ \frac{dy}{dx} = f(y)g(x) \] , where a, b, c are given constants and f is a function of x only?

In order to solve this problem, we first solve the homogeneous problem and then solve the inhomogeneous problem.

What is a homogeneous problem?

The linear differential equation is in the form \[ \frac{dy}{dx} = f(y)g(x) \] where .

What is an inhomogeneous (or nonhomogeneous) problem?

The linear differential equation is in the form \[ \frac{dy}{dx} = f(y)g(x) \] where .

Initial Conditions - We need two initial conditions to solve a second order problem.

Homogeneous Problems

Inhomogeneous Problems


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