Internal problem ID [873]
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: 2(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\left (1+y^{2}\right ) x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(diff(y(x),x) = x^2*(1+y(x)^2),y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\frac {x^{3}}{3}+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.171 (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*}