Internal problem ID [3114]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 366.
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 (3 x^{2}+a y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 48
dsolve(2*x^3*diff(y(x),x) = (3*x^2+a*y(x)^2)*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left (-a x +c_{1}\right ) x}\, x}{-a x +c_{1}} \\ y \relax (x ) = -\frac {\sqrt {\left (-a x +c_{1}\right ) x}\, x}{-a x +c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.186 (sec). Leaf size: 49
DSolve[2 x^3 y'[x]==(3 x^2+a y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^{3/2}}{\sqrt {-a x+c_1}} \\ y(x)\to \frac {x^{3/2}}{\sqrt {-a x+c_1}} \\ y(x)\to 0 \\ \end{align*}