Thread: Solving this differential equation..

Please,help is very much appreciated...
I am required to solve this second order ODE :
y"(x)-3y'(x)-2y(x)=sinh(x)

....using the Variation of Parameters method.
The final answer is EXTREMELY complicated,and i have no idea how to get to that answer.Its too long to be typed here.Would really appreciate the help.thanks.
Note: it is a parabolic sinh(x) , not just sin(x).

Originally Posted by tite

y"(x)-3y'(x)-2y(x)=sinh(x

Here.

thanks very much for your quick reply...
just one more question,what if i want the solution to be in terms of sinh and cosh ? how can i transform what you gave me into such?
thanks again.

Originally Posted by tite

thanks very much for your quick reply...
just one more question,what if i want the solution to be in terms of sinh and cosh ? how can i transform what you gave me into such?
thanks again.

That is a basic integration problem, what exactly is you difficutly?

Note that,
e^x-e^(-x)/e^(r_1 x)
Can be expressed as,
e^x/e^(r_1 x) - e^(-x)/e^(r_1 x) = e^(x-r_1 x) - e^(-x-r_1x)
Express as,
e^(x(1-r_1))-e^(-x(1+r_1))
You can integrate that.