# Solutions of Differential Equations with Initial Value Problems

Consider the initial-value problem y'''+9y'=0, y(0)=3, y'(0)=-1, y''(0)=2. Given that http://forums.cramster.com/Answer-Board/Image/cramster-equation-2006318224846327831888477500005072.gif [Broken] are three linearly independent solutions of the given homogeneous linear differential equation, determine the particular solution of the initial-value problem.

So far I have y=C1(1)+C2(cos3x)+C3(sin3x) so 3=C1+C2+C3sin9 Is that right? Please help

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## Answers and Replies

0rthodontist
Science Advisor
No, it isn't. You know y(0)=3 and what you want to do is substitute that in to y=C1(1)+C2(cos3x)+C3(sin3x) (which is correct). Doing that gives you
3 = c1(0) + C2(cos3*0) + C3(sin3*0).

OK, so then I would get C2 = 3, Then I would do the derivative of y and get -9sin3x+3c3cos3x, and use y'(0)=-1, so that would be -1=-9sin-3+3c3cos-3

0rthodontist
Science Advisor
No, what's the derivative of y, forget the C's for a minute.

HallsofIvy
Science Advisor
Homework Helper
In y(0)= 3, x= 0, not 3!! That was your mistake in your first post
sin(0)= 0, cos(0)= 1 so y(0)= 3 gives you C1+ C2= 3.

In "y'(0)= -1", x= 0, not -1!!!
3C3= -1.