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Question: Particular Solution and dsolve

Question:Particular Solution and dsolve

smokeybob 132 Maple
ode
September 17 2011
0

Hi there,

I have a de that I have gotten maple to solve using dsolve (y'''+2y''-11y'-12y)=48-28exp(3t). When the solution comes up however, the particular solution is in an odd form: 

(-4*exp(3*t)+(11/28)*exp(6*t)-t*exp(6*t))*exp(-3*t)

+_C1*exp(-4*t)+_C2*exp(-t)+_C3*exp(3*t)

However, the particular solution here contains part of the homogeneous solution inside of it: namely the 11/28exp(3t) term. Is there any way to run a function on my solution that basically checks to make sure the "particular solution" isn't just a constant multiple of one of my homogeneous solutions? Or do I just have to check manually?

-4+(11/28)*exp(3*t)-exp(3*t)*t+_C1*exp(-4*t)+_C2*exp(-t)+_C3*exp(3*t)

 
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