Internal problem ID [3113]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 365.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y^{\prime } x^{3}-\left (x^{2}-y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 26
dsolve(2*x^3*diff(y(x),x) = (x^2-y(x)^2)*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x}{\sqrt {c_{1} x -1}} \\ y \relax (x ) = -\frac {x}{\sqrt {c_{1} x -1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.239 (sec). Leaf size: 39
DSolve[2 x^3 y'[x]==(x^2-y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{\sqrt {-1+c_1 x}} \\ y(x)\to \frac {x}{\sqrt {-1+c_1 x}} \\ y(x)\to 0 \\ \end{align*}