# First order differential equation

• May 21st 2012, 11:51 AM
joceninja
First order differential equation
http://www.pluggakuten.se/mathsymbol...d2f27dd360.gif

find the solution that fulfills http://www.pluggakuten.se/mathsymbol...cca8bc8388.gif

please take me through the steps cause i dont know where to start all i can see is that it is separable and i didnt get how to solve it by reading in the book or solving the easier ones
• May 21st 2012, 11:57 AM
Sylvia104
Re: First order differential equation
$e^{2y}\frac{\mathrm dy}{\mathrm dx} = x+x^3$

$\Rightarrow\ \int e^{2y}\,\mathrm dy = \int x+x^3\,\mathrm dx$
• May 21st 2012, 12:03 PM
joceninja
Re: First order differential equation
Quote:

Originally Posted by Sylvia104
$e^{2y}\frac{\mathrm dy}{\mathrm dx} = x+x^3$

$\Rightarrow\ \int e^{2y}\,\mathrm dy = \int x+x^3\,\mathrm dx$

im with you so far but i dont see how im supposed to solve the http://www.pluggakuten.se/mathsymbol...cca8bc8388.gif
• May 21st 2012, 12:12 PM
Sylvia104
Re: First order differential equation
Do the integration first.
• May 21st 2012, 12:20 PM
joceninja
Re: First order differential equation
http://latex.codecogs.com/examples/2...8011374d4b.gif

like that or?
feels like im wrong cause i never really understood what you do when you take the dy/dx and take *dy on both sides so you get dy on left side and dx on right side etc.

cause i dont see how dy and dx just can move around since dy/dx=y'
• May 21st 2012, 01:06 PM
Sylvia104
Re: First order differential equation
$\int e^{2y}\,\mathrm dy = \int x+x^3\,\mathrm dx$

$\Rightarrow\ \frac{e^{2y}}2 = \frac{x^2}2 + \frac{x^4}4 + C$

Now substitute $x=0,y=0$ to find the constant $C.$
• May 21st 2012, 02:39 PM
joceninja
Re: First order differential equation
ahh ye my bad this is where i made the misstake e^(2y)

but cheers for the help!