Internal problem ID [5081]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page
114
Problem number: Example 3.1.
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: 0.003 (sec). Leaf size: 12
dsolve(diff(y(x),x)=x^2*(y(x)^2+1),y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\frac {x^{3}}{3}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.202 (sec). Leaf size: 30
DSolve[y'[x]==x^2*(y[x]^2+1),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*}