Now find the integrating factor.
Me agian, catch up on my DE HW...(150ish DE's in 4days ) im doing a linear prob.
Question: x^2(dy/dx) + x(x+2)y = e^x
I have found roe (p) and now im trying to intergrate the right side....i come up with... Dx[2x(e^x)y] = 2 (intergal sign)(x^-1)(e^2x)
ive tryed to use intergrating by parts....but it helps not as i get down to (above intregal) (intregal sign) (-x^(-2))x((1/2x)e^2x) and im back where i started..
The answer i need to get it to is....y= 1/2(x^-2)e^x+cx^-2(e^-x)
I'd appreciate any help...also any hints to what i did wrong
the biggest problem i get is when i go to intergrate the right side and use intergration by parts...i get u = x^-1 du= -x^-2 dv= e^2x V = 1/2 e^2x
but that brings me back to x^-1(1/2 e^2x) (intragal sign) (1/2e^2x)(x^-1)
which just gives me another parts intregal....almost the same one minus the constant multiplyer which wont really help anything
not really sure if i just doing my math wrong or which