Calculating first order differential equations.

y' = (x+2)^2e^y with y(1) = 0

Differential Equation

xy' + (1+x)y = 3 with y(4) = 50 I know the answer is y = (3 + 197e^4-x)/x, but am unsure how to get there.

To solve the problem by separation of variables

I have no idea how to start this problem. dN/dt + N = Nte^t+2 So far I have, dN/dt = Nte^t+2 - N where do I go from there.

Solving differential equations

Solve each of the following differential equations: ***For each problem,state the method you used and show the work required to obtain the answer.*** 1) (y-(cos^2)x)dx + cosxdy=0 2) ye^x dx= (4+e^2x)dy

Solve the differential equation

Please solve this equation d^2y/dx^2 - 4y = x^3 + 3