75.12.36 problem 310

Internal problem ID [16902]
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 : 310
Date solved : Tuesday, January 28, 2025 at 09:40:23 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.191 (sec). Leaf size: 28

dsolve(y(x)^3+2*(x^2-x*y(x)^2)*diff(y(x),x)=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: 2.897 (sec). Leaf size: 60

DSolve[y[x]^3+2*(x^2-x*y[x]^2)*D[y[x],x]==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*}