(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

y''-4y=60e^{4t}

y(0)=9 and y'(0)=2

2. Relevant equations

none in particular

3. The attempt at a solution

First I solved for the auxiliary equation.

r^{2}-4r

r(r-4)

r=0, 4

So the general solution for the homogenous form is C_{1}e^{0x}+C_{2}e^{4x}where C1 and C2 are unknown coefficients to be found.

The particular solution is calculating by considering Y_{p}= AXe^{4x}

Differentiating that twice, and solving for Yp, I get Yp=15xe^{4x}

So the general solution for this is obtained by adding the homogeneous and the particular. So I get: C_{1}e^{0x}+C_{2}e^{4x}+15xe^{4x}

I differentiated this equation and got 4C_{2}+15e^{4x}+60x^{4x}

So then I got 4C_{2}+15=2, so C2=-3.25

Also, from the general solution C1+C2=9, so C1=12.25

The final answer I got was (12.25)e^{0x}+-3.25e^{4x}+15xe^{4x}but this is wrong. Any ideas?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Undetermined Coefficients Initial Value Question

**Physics Forums | Science Articles, Homework Help, Discussion**