Need urgent help on laplace transform and PDE !

[reverie414]

I'm stuck with this 2 questions ...

 

q1) Using laplace transforms, solve: y" + 4y = r(t), where r(t) = {3sint, 0<t<pi, -3sint, t>pi y(0)=0, y'(0)=3.

 

this is what i get after rewriting for the step function: 3sint [1-u(t-pi)] + (-3sint)u(t-pi) ... im lost from then on.

 

q2) Using the method of seperation of variables, solve the following partial differential equations:

a)yux(subscript)-xuy(subscript)=0

b)ux(subscript)=yuy(subscript)

 

i'm really at my wits end ... need to submit shortly afterwards. thanks a lot for the help.

[CPL.Luke]

solve the first one as two different differential equations.

 

for the second one what level is this at, I assume no boundary conditions/ fourier knowledge is known?

 

if so than say that the solution is a product phi(x) psi(y) then try and get all the parts of the equation that depend on y on one side, and all of the ones that depend on x on the other. than you can claim that both sides have to be equal to a constant and thus you are solving two ode's that you should know how to do.