anonymous
  • anonymous
Find the solution of the differential equation y'= 2x/(1+x^4) , such that y(0)=0
Differential Equations
schrodinger
  • schrodinger
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Mimi_x3
  • Mimi_x3
\[\frac{dy}{dx}=\frac{2x}{1+x^4}\] just integrate both sides i suppose..
Mimi_x3
  • Mimi_x3
\[\int \frac{dy}{dx} = \int \frac{2x}{1+x^4}\]
anonymous
  • anonymous
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.

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Mimi_x3
  • Mimi_x3
I made a mistake.. trig substitution..or \(u=x^2\)
zugzwang
  • zugzwang
\[\frac{dy}{dx}=\frac{2x}{1+x^4}\]\[dy=\frac{2x}{1+x^4}dx\]
zugzwang
  • zugzwang
\[\int\limits_{}^{} dy=\int\limits_{}^{}\frac{2x}{1+x^4}dx\]

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