75.12.7 problem 281

Internal problem ID [16873]
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 : 281
Date solved : Tuesday, January 28, 2025 at 09:38:38 AM
CAS classification : [_Bernoulli]

\begin{align*} y-x y^{2} \ln \left (x \right )+x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

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

\[ y = -\frac {2}{\left (\ln \left (x \right )^{2}-2 c_{1} \right ) x} \]

✓ Solution by Mathematica

Time used: 0.160 (sec). Leaf size: 27

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

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