- #1
djeitnstine
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Homework Statement
[tex]y''+y=tan(x)+e^{3x}-1[/tex]
Homework Equations
homogeneous solution:
[tex]y_{hom..}=C_{1}cos(x)+C_{2}sin(x)[/tex]
particular solution:
[tex]y_{parti..}=v_{1}' cos(x)+v_{2}' sin(x)[/tex]
The Attempt at a Solution
[tex]v_{1}' cos(x)+v_{2}' sin(x)=0[/tex] (1)
[tex]-v_{1}' sin(x)+v_{2}' cos(x) = tan(x)+e^{3x}-1 [/tex] (2)
(1)* by sin (2)* by cos
and solve for v2
[tex]sin(x)+e^{3x}cos(x)-cos(x)=v_{2}'[/tex]
[tex]-cos(x)+ \frac{3}{10}e^{3x}cos(x)-\frac{1}{10}sin(x)-sin(x)=v_{2}[/tex]
Now finding v1 is the problem here. if I reverse the multiplication and do (1)* by cos (2)* by sin it seems even worse =(. I saw the complete answer and if I remember correctly its [tex]y_{p}=\frac{1}{2}cos(x)ln(sin(x)+1)-\frac{1}{2}cos(x)ln(sin(x)-1)-\frac{1}{10}e^{3x}+1[/tex]
I really just need to know what to multiply by to get going