# Math Help - First order differential equation

1. ## First order differential equation

find the solution that fulfills

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

2. ## Re: First order differential equation

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

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

3. ## Re: First order differential equation

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

4. ## Re: First order differential equation

Do the integration first.

5. ## Re: First order differential equation



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'

6. ## 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 $C.$

7. ## Re: First order differential equation

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

but cheers for the help!