Seperation of Variables (inc cos and exp)

**isp_of_doom** · February 9th 2010, 07:48 PM

Hi all,
Problem below:

Solve the following differential equation

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

I can re arrange this into:

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

From there integration brings:

$\ln|y| + c = \frac{sin(2x+1)}{2} + \frac{e^{3x}}{3} + c$

then multiplying by $e^{x}$ :

$y + c = e^{\frac{sin(2x+1)}{2} + \frac{e^{3x}}{3} + c}$

Now I'm stuck. I can't see any way to simplify the $e^{()}$ value on the right. It doesn't really feel solved to me... Is it?

**Soroban** · February 9th 2010, 08:52 PM

Hello, isp_of_doom!

Your first step is wrong . . .

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

We have: . $y\,dy \;=\;\left[\cos(2x+1) + e^{3x}\right]\,dx$

Integrate: . $\tfrac{1}{2}y^2 \;=\;\tfrac{1}{2}\sin(2x+1) + \tfrac{1}{3}e^{3x} + C$

. . . . . . . . . $y^2 \;=\;\sin(2x+1) + \tfrac{2}{3}e^{3x} + C$

Thread: Seperation of Variables (inc cos and exp)

LinkBack

Thread Tools

Display

Seperation of Variables (inc cos and exp)

Similar Math Help Forum Discussions

Seperation of variables.

Seperation of Variables

seperation of variables help

seperation of variables help

Seperation of Variables

Search Tags