Solve differential equation xy' + xy + 2y - 2e^(-x) = 0

I need help with the problem! xy' + xy + 2y - 2e^(-x) = 0 I had a hard time figuring out how to solve it... please help!

Non-linear differential equation word problem

Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A are used. It is observed that 10 grams of C are formed in 5 minutes. 1. How much is formed in 20 minutes? 2. What is the limiting amount of C after a long time? 3. How much of chemicals A and B remain after a long time? I originally set up the equation as DR/Dt = k(a-x)(b-x) where k is constant, a=amount of A, b= amount of B, and x = amount of C.

Solve: (e^(x)+y)dx + (2+x+y*e^(y))dy = 0 , y(0) = 1

Solve: (e^(x)+y)dx + (2+x+y*e^(y))dy = 0 , y(0) = 1

I can't figure out how to do this equation...is it separable or homogenous? (sqrt(x) +sqrt(y))^2dx = xdy, y(1) = 0

I can't figure out how to do this equation...is it separable or homogenous? (sqrt(x) +sqrt(y))^2dx = xdy, y(1) = 0

first order differential equations

Please solve the differential equation below. Please show all steps. dy/dx=(2x²+1)/(xe^y)