[SOLVED] integral of perfect derivative

**snaes** · February 15th 2010, 08:48 PM

The Differential Equation: $3y^2 y''(x) + 2e^y y'(x)+2y y'(x)+6y(y'(x))^2=0$ is a perfect derivative. Find the first integral.
$3y^2 \dfrac{d^2y}{dx^2} + 2e^y \dfrac{dy}{dx} + 2y \dfrac{dy}{dx}+6y(\dfrac{dy}{dx})^2=0$

not sure which notation is best so i put 2 ways of the same problem.

This is the product rule split up but i just cannot see how to do this backwards. Any help would be great! Thanks.

**mr fantastic** · February 15th 2010, 09:42 PM

Originally Posted by snaes

The Differential Equation: $3y^2 y''(x) + 2e^y y'(x)+2y y'(x)+6y(y'(x))^2=0$ is a perfect derivative. Find the first integral.
$3y^2 \dfrac{d^2y}{dx^2} + 2e^y \dfrac{dy}{dx} + 2y \dfrac{dy}{dx}+6y(\dfrac{dy}{dx})^2=0$

not sure which notation is best so i put 2 ways of the same problem.

This is the product rule split up but i just cannot see how to do this backwards. Any help would be great! Thanks.

I suspect there's a typo in the question. I think it should be
$3y^2 \dfrac{d^2y}{dx^2} + 2e^y \dfrac{dy}{dx} + 2y {\color{red} e^y} \dfrac{dy}{dx}+6y(\dfrac{dy}{dx})^2=0$ .

**snaes** · February 16th 2010, 09:49 AM

That would definately help. I think its a typo as well. Thanks.

**Danny** · February 16th 2010, 09:57 AM

There might be a typo but for your original problem, you could have

$<br /> \frac{d}{dx}\left( 3 y^2 y' + 2 e^y + y^2\right) = 0.<br />$

**snaes** · February 16th 2010, 12:43 PM

Yeah, the problem had a typo, but its fixed now thanks.

Thread: [SOLVED] integral of perfect derivative

LinkBack

Thread Tools

Display

[SOLVED] integral of perfect derivative

Similar Math Help Forum Discussions

[SOLVED] derivative of integral

[SOLVED] Simplifying perfect squares

not a perfect derivative

[SOLVED] Derivative of an integral

[SOLVED] Practice and reward makes things perfect!

Search Tags