Internal problem ID [882]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 1, Introduction. Section 1.2 Page 14
Problem number: 5(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-x \left (1+y^{2}\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.042 (sec). Leaf size: 10
dsolve([diff(y(x),x) = x*(1+y(x)^2),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\frac {x^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.201 (sec). Leaf size: 13
DSolve[{y'[x] ==x*(1+y[x]^2),y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan \left (\frac {x^2}{2}\right ) \\ \end{align*}