Integrating x^5.ln(x) in first order linear differential equation

[mr bob]

Just need a hand with this one.

(dy/dx)x + 2y = x^3.ln(x)

(dy/dx) = (x^3.ln(x) - 2y)/x

Integrating factor = x^2

(dy/dx)x^2 + 2xy = (x^3.ln(x))x^2

yx^2 = INT[(x^3.ln(x))x^2]

I'm having trouble integrating the last part to complete it.

Thanks a lot and in advance for any help.

 

[quantumdude]

Integrating factor = x^2

Correct.

(dy/dx)x^2 + 2xy = (x^3.ln(x))x^2

Check this line again. You should have $x^4\ln(x)$ on the right side. You have an extra power of $x$ there.

yx^2 = INT[(x^3.ln(x))x^2]

I'm having trouble integrating the last part to complete it.

Once you clean up the right side you should integrate by parts. If you choose wisely for the parts you will only have to do it once.

 

[mr bob]

Thank you Tom. These differential equations can be a little tough sometimes.