Internal problem ID [3099]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 351.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x^{3}-\left (2 x^{2}+y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(x^3*diff(y(x),x) = (2*x^2+y(x)^2)*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{2}}{\sqrt {-x^{2}+c_{1}}} \\ y \relax (x ) = -\frac {x^{2}}{\sqrt {-x^{2}+c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.167 (sec). Leaf size: 47
DSolve[x^3 y'[x]==(2 x^2+y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2}{\sqrt {-x^2+c_1}} \\ y(x)\to \frac {x^2}{\sqrt {-x^2+c_1}} \\ y(x)\to 0 \\ \end{align*}