Thread: another DE problem (well more of a parts prob)

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

Now find the integrating factor.

i got to there....my intergrating factor came out to be....2x(e^x)

I think the integrating factor should be

Show your process to find it.

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

(x+2)/x -> 1+2/x

e^(intregal) 1+2/x -> x+ 2ln lxl -> e and ln cancel leaving 2xe^x

oh duh.....sorry, i havent used log, ln and "e" in ages....forgot all the rules. know a good place to brezze back up on em?

It's quite dangerous solving differential equations if you don't consider the basic properties.

I've got to go now, but I hope someone could give you a 'refresh'

Greetings