# Verify the solution of the differential equation. NOTE: Observe a structure of the solution, then...

## Question:

Verify the solution of the differential equation.

NOTE: Observe a structure of the solution, then use appropriate rules.

{eq}y" - 5y' + 4y = 0 {/eq}

Solution {eq}y = e^{4x} {/eq}

## Differential Equation:

The equation can be found by replacing y by operator D and then finding the roots of the new equation. We will get the two roots. Then from the roots, we can write the general equation involving two constants.

## Answer and Explanation: 1

To solve the differential equation we will replace the double derivative of y by {eq}D^{2} {/eq}, the single derivative of y by D and then put it equal to 0.

Let us now find the roots of the equation

{eq}y''-5y'+4y=0\\ D^{2}-5D+4=0\\ D=1,4 {/eq}

The roots of the equation are 1,4

Now writing the general equation we get

{eq}y=c_{1}e^{x}+c_{2}e^{4x} {/eq}

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question