Internal problem ID [14976]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 4. Equations with variables separable and equations reducible to them. Exercises
page 38
Problem number: 49.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{2}-y^{\prime } x=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve((1+y(x)^2)=x*diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\ln \left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.167 (sec). Leaf size: 25
DSolve[(1+y[x]^2)==x*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan (\log (x)+c_1) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}