Question

I am having trouble finishing this differential equation: (dy/dx) + xy = x , where i found the I.F. and towards the end after i did the UV method, but i am stuck at integration of {xe^((x^2)/2)) }dx

Answer 1

dy/dx=x-xy
dy/dx=x(1-y)
dy(1-y)=xdx
-1/2y^2 +y= 1/2x^2 +C

Answer 2

Lets see here, you went from dy/dx=x(1-y) and then got dy/(1-y)=xdx right? From there you can integrate to get -ln|1-y|=(1/2)x^2.

From there you get y=1-e^(-(x^2)/2), does that make sense? I can explain it better if you need, but you'er integrating twice at the same time.

Answer 3

myko the integral become dy/(1-y) not dy(1-y).

Answer 4

ups, :)

Answer 5

so i dont need the integrating factor, becuase i am able to do it by variable seperable technique?

Answer 6

and how did you get -1/2y^2 +y?

Answer 7

myko did the math wrong, so immeen it doesn't become -1/2y^2+y