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petapan123
Find the solution of the differential equation y'= 2x/(1+x^4) , such that y(0)=0
\[\frac{dy}{dx}=\frac{2x}{1+x^4}\] just integrate both sides i suppose..
\[\int \frac{dy}{dx} = \int \frac{2x}{1+x^4}\]
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.
I made a mistake.. trig substitution..or \(u=x^2\)
\[\frac{dy}{dx}=\frac{2x}{1+x^4}\]\[dy=\frac{2x}{1+x^4}dx\]
\[\int\limits_{}^{} dy=\int\limits_{}^{}\frac{2x}{1+x^4}dx\]