Internal problem ID [130]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-1-x^{2}-y^{2}-x^{2} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 13
dsolve(diff(y(x),x) = 1+x^2+y(x)^2+x^2*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\frac {1}{3} x^{3}+c_{1}+x \right ) \]
✓ Solution by Mathematica
Time used: 0.204 (sec). Leaf size: 17
DSolve[y'[x] == 1+x^2+y[x]^2+x^2*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan \left (\frac {x^3}{3}+x+c_1\right ) \\ \end{align*}