Internal problem ID [942]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-2 x y \left (1+y^{2}\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.055 (sec). Leaf size: 16
dsolve([diff(y(x),x)=2*x*y(x)*(1+y(x)^2),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{\sqrt {2 \,{\mathrm e}^{-2 x^{2}}-1}} \]
✓ Solution by Mathematica
Time used: 2.275 (sec). Leaf size: 27
DSolve[{y'[x]==2*x*y[x]*(1+y[x]^2),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {i e^{x^2}}{\sqrt {e^{2 x^2}-2}} \\ \end{align*}