Internal problem ID [3424]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 685.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (3 x^{2}+2 y^{2}\right ) y y^{\prime }+x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 137
dsolve((3*x^2+2*y(x)^2)*y(x)*diff(y(x),x)+x^3 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-8 x^{2} c_{1}^{2}-2 \sqrt {8 x^{2} c_{1}^{2}+1}+2}}{4 c_{1}} \\ y \relax (x ) = \frac {\sqrt {-8 x^{2} c_{1}^{2}-2 \sqrt {8 x^{2} c_{1}^{2}+1}+2}}{4 c_{1}} \\ y \relax (x ) = -\frac {\sqrt {-8 x^{2} c_{1}^{2}+2 \sqrt {8 x^{2} c_{1}^{2}+1}+2}}{4 c_{1}} \\ y \relax (x ) = \frac {\sqrt {-8 x^{2} c_{1}^{2}+2 \sqrt {8 x^{2} c_{1}^{2}+1}+2}}{4 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 17.02 (sec). Leaf size: 253
DSolve[(3 x^2+2 y[x]^2)y[x] y'[x]+x^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-4 x^2-\sqrt {8 e^{2 c_1} x^2+e^{4 c_1}}+e^{2 c_1}}}{2 \sqrt {2}} \\ y(x)\to \frac {\sqrt {-4 x^2-\sqrt {8 e^{2 c_1} x^2+e^{4 c_1}}+e^{2 c_1}}}{2 \sqrt {2}} \\ y(x)\to -\frac {\sqrt {-4 x^2+\sqrt {8 e^{2 c_1} x^2+e^{4 c_1}}+e^{2 c_1}}}{2 \sqrt {2}} \\ y(x)\to \frac {\sqrt {-4 x^2+\sqrt {8 e^{2 c_1} x^2+e^{4 c_1}}+e^{2 c_1}}}{2 \sqrt {2}} \\ y(x)\to \text {Undefined} \\ y(x)\to -\frac {\sqrt {-x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-x^2}}{\sqrt {2}} \\ \end{align*}