# Thread: find the general solution

1. ## find the general solution

I was told to find the general solution to this problem:

I rearranged it to put it in standard form and got:

dy/dx + 2x^4 (y) = -x^5 +x^2 + 4x -3

then, finding mu(x) = e^(intergral of (2x^4)dx)

multiplying both sides by mu(x), then solving for y(x), I eventually got:

y(x) = (1/5)(1/e^((2x^5)/5)) * [intergral of (mu(x) * (-x^5 +x^2 + 4x - 3)dx]

this is about where I get stuck. This intergral is a monster!!!

I've tried multiplying through, then doing each individual intergral, but... its still aweful. Am I doing something wrong?

2. Originally Posted by fruitbodywash
I was told to find the general solution to this problem:

I rearranged it to put it in standard form and got:

dy/dx + 2x^4 (y) = -x^5 +x^2 + 4x -3

then, finding mu(x) = e^(intergral of (2x^4)dx)

multiplying both sides by mu(x), then solving for y(x), I eventually got:

y(x) = (1/5)(1/e^((2x^5)/5)) * [intergral of (mu(x) * (-x^5 +x^2 + 4x - 3)dx]

this is about where I get stuck. This intergral is a monster!!!

I've tried multiplying through, then doing each individual intergral, but... its still aweful. Am I doing something wrong?
Dear fruitbodywash,

How did you got, dy/dx + 2x^4 (y) = -x^5 +x^2 + 4x -3 I think there is a mistake.

But you could rearrange this as,

$\displaystyle (x^{5}+5)\frac{dy}{dx}=x^2+4x-3-10x^{4}y$

$\displaystyle \frac{dy}{dx}+\left(\frac{10x^{4}}{x^{5}+5}\right) y=x^{2}+4x-3$

This is a linear differential equation and could be solved using the method you have used.