75.4.2 problem 47

Internal problem ID [16704]
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
Date solved : Tuesday, January 28, 2025 at 09:18:48 AM
CAS classification : [_separable]

\begin{align*} 1+y^{2}+x y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 34

dsolve((1+y(x)^2)+(x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {\sqrt {-x^{2}+c_{1}}}{x} \\ y &= -\frac {\sqrt {-x^{2}+c_{1}}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.343 (sec). Leaf size: 96

DSolve[(1+y[x]^2)+(x*y[x])*D[y[x],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*}