Internal problem ID [43]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-1+x^{2}-y^{2}+x^{2} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 19
dsolve(x^2*diff(y(x),x) = 1-x^2+y(x)^2-x^2*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = -\tan \left (\frac {x c_{1}+x^{2}+1}{x}\right ) \]
✓ Solution by Mathematica
Time used: 0.262 (sec). Leaf size: 17
DSolve[x^2*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 (x+\frac {1}{x}-c_1\right ) \\ \end{align*}