Internal problem ID [3936]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 689.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {\left (x^{3}+a y^{3}\right ) y^{\prime }-x^{2} y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 23
dsolve((x^3+a*y(x)^3)*diff(y(x),x) = x^2*y(x),y(x), singsol=all)
\[ y \left (x \right ) = {\left (\frac {1}{a \operatorname {LambertW}\left (\frac {c_{1} x^{3}}{a}\right )}\right )}^{\frac {1}{3}} x \]
✓ Solution by Mathematica
Time used: 18.61 (sec). Leaf size: 113
DSolve[(x^3+a y[x]^3)y'[x]==x^2 y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{\sqrt [3]{a} \sqrt [3]{W\left (\frac {x^3 e^{-\frac {3 c_1}{a}}}{a}\right )}} y(x)\to -\frac {\sqrt [3]{-1} x}{\sqrt [3]{a} \sqrt [3]{W\left (\frac {x^3 e^{-\frac {3 c_1}{a}}}{a}\right )}} y(x)\to \frac {(-1)^{2/3} x}{\sqrt [3]{a} \sqrt [3]{W\left (\frac {x^3 e^{-\frac {3 c_1}{a}}}{a}\right )}} y(x)\to 0 \end{align*}