60.1.300 problem 301

Internal problem ID [10314]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 301
Date solved : Monday, January 27, 2025 at 07:08:05 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (6 x y^{2}+x^{2}\right ) y^{\prime }-y \left (3 y^{2}-x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.059 (sec). Leaf size: 38

dsolve((6*x*y(x)^2+x^2)*diff(y(x),x)-y(x)*(3*y(x)^2-x)=0,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{\frac {3 c_{1}}{2}} \sqrt {6}}{6 x \sqrt {\frac {{\mathrm e}^{3 c_{1}}}{x^{3} \operatorname {LambertW}\left (\frac {6 \,{\mathrm e}^{3 c_{1}}}{x^{3}}\right )}}} \]

✓ Solution by Mathematica

Time used: 3.481 (sec). Leaf size: 73

DSolve[(6*x*y[x]^2+x^2)*D[y[x],x]-y[x]*(3*y[x]^2-x)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2+3 c_1}}{x^3}\right )}}{\sqrt {6}} \\ y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2+3 c_1}}{x^3}\right )}}{\sqrt {6}} \\ y(x)\to 0 \\ \end{align*}