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

Re: First order differential equation

$\displaystyle e^{2y}\frac{\mathrm dy}{\mathrm dx} = x+x^3$

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

Re: First order differential equation

Quote:

Originally Posted by

**Sylvia104** $\displaystyle e^{2y}\frac{\mathrm dy}{\mathrm dx} = x+x^3$

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

im with you so far but i dont see how im supposed to solve the http://www.pluggakuten.se/mathsymbol...cca8bc8388.gif

Re: First order differential equation

Do the integration first.

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'

Re: First order differential equation

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

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

Now substitute $\displaystyle x=0,y=0$ to find the constant $\displaystyle C.$

Re: First order differential equation

ahh ye my bad this is where i made the misstake e^(2y)

but cheers for the help!