# Thread: Particular Solution to Differential Equation!!!

1. ## Particular Solution to Differential Equation!!!

Hi, I am having trouble trying to figure out the last part. Given the initial conditions, I need to find a solution to the equation.

Problem:

Consider the differential equation
(where primes indicate derivatives with respect to x). Find a particular solution to the differential equation having the form
using the method of Variation of Parameters. In this, (Note that this asks for and , not and !)
e^(-4x)

e^(3x)

-1

e^(-7x)

I am find upto this point.

TROUBLE WITH THE FOLLOWING PART:

Then use your solution to find a solution to the differential equation that satisfies the initial conditions , .

This is where I am stuck. The solution is not right...

Thanks

-x^e(-4x) -1/7e^(-4x)+1/7 e^(3x)

u1 ' = -1 u1 = -x +A

u2 ' = e^(-7x) u2 = -1/7e^(-7x) + B

y = -xe^(-4x) - 1/7 e^(-7x) + A e^(-4x) + B e^(3x)

Applying IC A + B = 1/7

-4A + 3B = 3/7

Multiply the top by 4 and add to the bottom you get B = 1/7, A = 0

-x^e(-4x) -1/7e^(-4x)+1/7 e^(3x) follows

3. ## Thanks!!!

Thanks very much!!!