1. ## integrate

How can integrate the following

$\displaystyle dy/dx = ( 5x^3 + 7y + 5 )^2$

2. Originally Posted by TGASJOOL
How can integrate the following

$\displaystyle dy/dx = ( 5x^3 + 7y + 5 )^2$
Expand the square on the right giving you a sixth order polynomial in x, then integrate term by term

CB

3. i forgot to mention

i should use a substitution

$\displaystyle u = ( 5x^3 + 7y + 5 )$

4. Originally Posted by CaptainBlack
Expand the square on the right giving you a sixth order polynomial in x, then integrate term by term

CB
Since there is a term with y in it on the right hand side, it's possible that the real question is not to integrate but to solve a differential equation. The OP will need to clarify the situation.

Originally Posted by TGASJOOL
i forgot to mention

i should use a substitution

$\displaystyle u = ( 5x^3 + 7y + 5)$

See my remark above.

5. Originally Posted by TGASJOOL
i forgot to mention

i should use a substitution

$\displaystyle u = ( 5x^3 + 7y + 5 )$

In which case differentiate then you have:

$\displaystyle \dfrac{du}{dx}=15x^2+7\dfrac{dy}{dx}=15x^2+7u^2$

or:

$\displaystyle \dfrac{du}{dx}-7u^2=15x^2$

which you need to solve

CB

6. Originally Posted by TGASJOOL
i forgot to mention

i should use a substitution

$\displaystyle u = ( 5x^3 + 7y + 5 )$