Internal problem ID [3094]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 346.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x^{3}-y \left (x^{2}+y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(x^3*diff(y(x),x) = y(x)*(x^2+y(x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{c_{1} x +1} \]
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 22
DSolve[x^3 y'[x]==y[x](x^2+y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{1+c_1 x} \\ y(x)\to 0 \\ \end{align*}