Particular Solution Using Undetermined Coeff.

[jenn9580]

I have the inhomogeneous DE: y''-4y'-5y=-2sinx-10cosx
I am not sure what trial particular solution I should use to find the coefficients.I know that for sinx or cosx I would use Acosx + Bsinx but I am not sure what I need to use since I have both.

 

[Deleted member 4993]

I have the inhomogeneous DE: y''-4y'-5y=-2sinx-10cosx
I am not sure what trial particular solution I should use to find the coefficients.I know that for sinx or cosx I would use Acosx + Bsinx but I am not sure what I need to use since I have both.

What are the solutions to the homogeneous part of the equation?

 

[jenn9580]

Sorry. y(x)=Asin(x)+Bcos(x)

 

[Deleted member 4993]

Sorry. y(x)=Asin(x)+Bcos(x)

Are you sure?

Does that satisfy your original homogeneous ODE;

y'' - 4y' - 5y = 0

according my calculations

y[sub:3n24u3h4]H[/sub:3n24u3h4] = Ae[sup:3n24u3h4]-x[/sup:3n24u3h4] + Be[sup:3n24u3h4]5x[/sup:3n24u3h4]

.

 

[jenn9580]

Thank you. I finally asked about it today & my professor cleared up what he was actually asking. Yes, that is the general solution, then I had to use the Asinx +Bcosx to find the undetermined coefficients & then the particular solution.