# Find the general solution of y''-12y'+36y=0 and also find the solution that satisfies the initial...

## Question:

Find the general solution of {eq}y''-12y'+36y=0 {/eq} and also find the solution that satisfies the initial conditions {eq}y(0)=5 {/eq} and {eq}y'(0)=0 {/eq}.

## Solve the Differential Equation:

Differential equation of form {eq}\phi \left(D\right)y=f\left(x\right) {/eq} has solution in two parts i.e complementary function {eq}y_c {/eq} and particular integral {eq}y_p {/eq}.

Use the initial conditions to find the values of constants.

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Given equation is

{eq}\displaystyle y''-12y'+36y=0 {/eq}

==> {eq}\displaystyle \frac{d^2y}{dx^2}-12\:\frac{dy}{dx}+36y=0 {/eq}

==>...

First-Order Linear Differential Equations

from

Chapter 16 / Lesson 3
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In this lesson you'll learn how to solve a first-order linear differential equation. We first define what such an equation is, and then we give the algorithm for solving one of that form. Specific examples follow the more general description of the method.