Solving a Differential Equation

[Jbreezy]

Homework Statement

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

Homework Equations

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

 

[pasmith]

Homework Statement

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

Homework Equations

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

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

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

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

 

[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?

 

[Dick]

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?

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

 

[Jbreezy]

OK. I kept looking over and it and I could not see where my math was wrong you know?
Hey I'm going to post another thread can you please help me ? It is solving a differential equation.

 

[Dick]

OK. I kept looking over and it and I could not see where my math was wrong you know?
Hey I'm going to post another thread can you please help me ? It is solving a differential equation.

Sure, if I'm still around. Somebody else could probably handle it too.