Internal problem ID [3326]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 584.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _exact, _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y y^{\prime } x^{3}+a +3 x^{2} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 36
dsolve(2*x^3*y(x)*diff(y(x),x)+a+3*x^2*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left (-a x +c_{1}\right ) x}}{x^{2}} \\ y \relax (x ) = -\frac {\sqrt {\left (-a x +c_{1}\right ) x}}{x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 44
DSolve[2 x^3 y[x] y'[x]+a+3 x^2 y[x]^2 ==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-a x+c_1}}{x^{3/2}} \\ y(x)\to \frac {\sqrt {-a x+c_1}}{x^{3/2}} \\ \end{align*}