# Thread: HW General Solution for Differential Equation

1. ## HW General Solution for Differential Equation

I do not know why my answer is wrong. I keep doing the problem again and again and get the same answer...

r''(t)=<e^t,sint,cost>
r'(t)=<e^t,cost,-sint>
r(t)=<e^t,-sint,-cost>

r(0) =<1,0,-1> + c2 = <4,0,5> ---> c2 = <3,0,6>
r'(0)=<1,1,0> +c1 = <0,3,5> --> c1=<-1,2,5>

ANS: r(t)=<e^t-t+3,-sint+2t,-cost+5t+6>

2. ## Re: HW General Solution for Differential Equation

Originally Posted by lc99

I do not know why my answer is wrong. I keep doing the problem again and again and get the same answer...

r''(t)=<e^t,sint,cost>
r'(t)=<e^t,cost,-sint>
r(t)=<e^t,-sint,-cost>

r(0) =<1,0,-1> + c2 = <4,0,5> ---> c2 = <3,0,6>
r'(0)=<1,1,0> +c1 = <0,3,5> --> c1=<-1,2,5>

ANS: r(t)=<e^t-t+3,-sint+2t,-cost+5t+6>
I get $r(t)=\left<e^t-t+3,4t-\sin(t).-\cos(t)+5t+6\right>$

3. ## Re: HW General Solution for Differential Equation

Oh my god, I did the derivative twice instead of the integral... Thanks!