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 https://instruct.math.lsa.umich.edu/...3d4ed66881.png and https://instruct.math.lsa.umich.edu/...949f7bca61.png, ***not** https://instruct.math.lsa.umich.edu/...56953d8751.png and https://instruct.math.lsa.umich.edu/...8be6464c61.png!)

https://instruct.math.lsa.umich.edu/...eea7c159f1.png e^(-4x)

https://instruct.math.lsa.umich.edu/...6f077d7a51.png e^(3x)

https://instruct.math.lsa.umich.edu/...563e53dda1.png -1

https://instruct.math.lsa.umich.edu/...8d6b5a5841.png 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 https://instruct.math.lsa.umich.edu/...b73d5ba911.png, https://instruct.math.lsa.umich.edu/...00c5753de1.png.

https://instruct.math.lsa.umich.edu/...b39caf0291.png https://instruct.math.lsa.umich.edu/...1151586451.png

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

Please help me out,

Thanks