Hi again. I was having some trouble with this implicit differentiation problem and was wondering if I could get some help.

$\displaystyle \frac{dy}{dx} - (3 + 2x)(1 + y^2) = 0$

Thanks

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- Oct 25th 2009, 02:30 AMDanogImplicit Differentiation
Hi again. I was having some trouble with this implicit differentiation problem and was wondering if I could get some help.

$\displaystyle \frac{dy}{dx} - (3 + 2x)(1 + y^2) = 0$

Thanks - Oct 25th 2009, 02:42 AMMush
- Oct 25th 2009, 02:51 AMDanog
Agh, my bad. The questions asks to find the general solution to the equation, and to express y as a function of x.

- Oct 25th 2009, 02:53 AMramiee2010
- Oct 25th 2009, 02:55 AMMush
- Oct 25th 2009, 03:20 AMProve It
You use the lazy notation :P.

To be COMPLETELY correct...

$\displaystyle \frac{dy}{dx} = (3 + 2x)(1 + y^2)$

$\displaystyle \frac{1}{1 + y^2}\,\frac{dy}{dx} = 3 + 2x$

$\displaystyle \int{\frac{1}{1 + y^2}\,\frac{dy}{dx}\,dx} = \int{3 + 2x\,dx}$

$\displaystyle \int{\frac{1}{1 + y^2}\,dy} = 3x + x^2 + C_1$

$\displaystyle \arctan{y} + C_2 = 3x + x^2 + C_1$

$\displaystyle \arctan{y} = 3x + x^2 + C$, where $\displaystyle C = C_1 - C_2$

$\displaystyle y = \tan{(3x + x^2 + C)}$. - Oct 25th 2009, 03:34 AMramiee2010
- Oct 25th 2009, 03:41 AMProve It