75.5.17 problem 116

Internal problem ID [16753]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 5. Homogeneous equations. Exercises page 44
Problem number : 116
Date solved : Tuesday, January 28, 2025 at 09:21:13 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} 2 x y^{\prime } \left (x -y^{2}\right )+y^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.185 (sec). Leaf size: 28

dsolve(2*x*diff(y(x),x)*(x-y(x)^2)+y(x)^3=0,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{\frac {c_{1}}{2}}}{\sqrt {-\frac {{\mathrm e}^{c_{1}}}{x \operatorname {LambertW}\left (-\frac {{\mathrm e}^{c_{1}}}{x}\right )}}} \]

✓ Solution by Mathematica

Time used: 2.900 (sec). Leaf size: 60

DSolve[2*x*D[y[x],x]*(x-y[x]^2)+y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -i \sqrt {x} \sqrt {W\left (-\frac {e^{c_1}}{x}\right )} \\ y(x)\to i \sqrt {x} \sqrt {W\left (-\frac {e^{c_1}}{x}\right )} \\ y(x)\to 0 \\ \end{align*}