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1. Find the general solution y(x) of the following differential equation. (20%)
(-3x+ y+6)dx+ (x+ y+2)dy
=
02. Find the general solution y(x) of the following differential equation. (20%)
d 2y dy .
- - 4 - + 3 y =sm2x dx2 dx
3. Find the general solution y(x) of the following differential equation. (20%)
4. Solve the following initial value problem by laplace transform only. (20%)
5. Solve the following partial differential equation where L is constant. (20%)
Boundary conditions: u(O,t)
=
O,u(L,t)=
0. {1,O<X<L/2 Initial conditions: u(x,O) =
O,L/2<x<O