Internal problem ID [933]
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: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-x^{2} \left (1+y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 12
dsolve(diff(y(x),x)= x^2*(1+y(x)^2),y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\frac {x^{3}}{3}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.167 (sec). Leaf size: 30
DSolve[y'[x]== x^2*(1+y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan \left (\frac {x^3}{3}+c_1\right ) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}