Homework Help: Linear diffy q

1. Oct 30, 2013

Jbreezy

1. The problem statement, all variables and given/known data

Solve the differential equation
x(dy/dx) -4y = x^4e^x

2. Relevant equations

3. The attempt at a solution

So this is what I did.

dy/dx -4y/x = x^3e^x

Then I did the integral of P(x) which I said was 4/x so the integral is lnx^4 then I(x) = e^lnx^4 = x^4. I then multiplied through by this and got

x^4(dy/dx) - 4x^3(y) = x^7e^x I said my product rule for my left side was (x^4(y))' so I ended up with x^4(y) = ∫ x^7(e^x) I just used a reduction formula for the integral. But is my procss OK? THanks
my equation b

2. Oct 30, 2013

pasmith

In this case $P(x) = -4/x$, so you've lost a minus sign in an exponent.

Try again with the correct $P(x)$.

3. Oct 30, 2013

Jbreezy

Hey dude, So I did but it doesn't seem right I made P(x) as you say so my integrating factor become I(x) = 1/x^4

I multiply though and my expression becomes

(1/x^4)(dy/dx) - 4y/x^5 = e^x/x OK so the left side is then....

(y/x^4)' = e^x /x
But if you try and integrate the right side you have to do the err function. That can't be right because my book isn't that advanced. So Did I do something wrong?

4. Oct 30, 2013

Dick

No, you did everything right. And yes, you don't get an elementary integral. It's not err it's Ei, but same problem.

5. Oct 30, 2013

Jbreezy

OK. I kept looking over and it and I could not see where my math was wrong you know?