Ordinary differential equations

Ok, can someone check my qorking is sound for these please? ta

question is to find the solution of:

dy/dx - (y^2)/(x+1)=0

For which y=1 at x=0

i've got y^-2 dy = (x+1)^-1 dx

Then integrated both sides to get

-y^-1 = ln|x+1| + constant

which ends with the equation

y = -(ln|x+1|-1)^-1.

number 2

general solution of:

dx/dt + x =e^t

ive got it as:

Sdx + S(x)dt=S(e^t) dt

To give an answer of

x(t+1) = e^t +c

which doesnt seem right or is it?

Final one which i could do with a few pointers on is

(dw/dx)sin x -wcosx = xsin^2 x

find an integrating factor u(x)

could you clarify this please?

I'm afraid i dont understand your reasoning, would i tbe possible to provide a step by step working? also, what do you mean by Aexp? thanks a lot