## petapan123 3 years ago Find the solution of the differential equation y'= 2x/(1+x^4) , such that y(0)=0

1. Mimi_x3

$\frac{dy}{dx}=\frac{2x}{1+x^4}$ just integrate both sides i suppose..

2. Mimi_x3

$\int \frac{dy}{dx} = \int \frac{2x}{1+x^4}$

3. Spacelimbus

if $\Large u= 1 + x^4$ then $\Large \frac{du}{dx}=4x^3$ How would you continue there? I am just curious, please don't misunderstand this, I know that there are plenty of ways to solve such an equation.

4. Mimi_x3

I made a mistake.. trig substitution..or $$u=x^2$$

5. zugzwang

$\frac{dy}{dx}=\frac{2x}{1+x^4}$$dy=\frac{2x}{1+x^4}dx$

6. zugzwang

$\int\limits_{}^{} dy=\int\limits_{}^{}\frac{2x}{1+x^4}dx$