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.
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