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 ...continues

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)

differential equations

Please solve the differential equation below. Please show all steps in the solution. √x dy/dx= e^(y+√x)

differential equations

Please solve the differential equation below. Please show all steps in the solution. 2 dy/dx - y = e^(x/2)

linear first order differential equation

Please solve the differential equation below. Please show each step. Thank you. e^(2x)y' + 2e^(2x)y = 2x

linear first order differential equation

Please help me solve this equation. I worked it out but am not sure of my answer or if I can simplify it. I used the four step method of solving a linear first order equation, so if you could solve it in the same manner, it would be appreciated. Thank you. (t+1)ds/dt +2s=3(t+1) + 1/(t+1)^2

first order differential equations

Please solve the following differential equation, showing all steps and substitutions. Thank you. tanθdr/dθ + r = sin²θ