75.12.19 problem 293

Internal problem ID [16885]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 293
Date solved : Tuesday, January 28, 2025 at 09:39:36 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 28

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

\begin{align*} y &= \sqrt {2 \ln \left (x \right )+c_{1}}\, x \\ y &= -\sqrt {2 \ln \left (x \right )+c_{1}}\, x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.183 (sec). Leaf size: 36

DSolve[(x^2+y[x]^2)-x*y[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x \sqrt {2 \log (x)+c_1} \\ y(x)\to x \sqrt {2 \log (x)+c_1} \\ \end{align*}