Internal problem ID [14974]
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: 47.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{2}+x y y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve((1+y(x)^2)+(x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {-x^{2}+c_{1}}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {-x^{2}+c_{1}}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.347 (sec). Leaf size: 96
DSolve[(1+y[x]^2)+(x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x^2+e^{2 c_1}}}{x} \\ y(x)\to \frac {\sqrt {-x^2+e^{2 c_1}}}{x} \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to \frac {x}{\sqrt {-x^2}} \\ y(x)\to \frac {\sqrt {-x^2}}{x} \\ \end{align*}