75.12.21 problem 295

Internal problem ID [16887]
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 : 295
Date solved : Tuesday, January 28, 2025 at 09:39:44 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

\[ y = -\frac {2 x}{x^{2}-2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 23

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

\begin{align*} y(x)\to -\frac {2 x}{x^2-2 c_1} \\ y(x)\to 0 \\ \end{align*}