Question

Find the solution of the differential equation

y'= 2x/(1+x^4) , such that y(0)=0

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

I made a mistake..
trig substitution..or \(u=x^2\)

Answer 5

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

Answer 6

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