Internal problem ID [3420]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 681.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 119
dsolve((3*x^2+y(x)^2)*y(x)*diff(y(x),x)+x*(x^2+3*y(x)^2) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-3 c_{1} x^{2}-\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} \\ y \relax (x ) = \frac {\sqrt {-3 c_{1} x^{2}+\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} \\ y \relax (x ) = -\frac {\sqrt {-3 c_{1} x^{2}-\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} \\ y \relax (x ) = -\frac {\sqrt {-3 c_{1} x^{2}+\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.375 (sec). Leaf size: 245
DSolve[(3 x^2+y[x]^2)y[x] y'[x]+x(x^2+3 y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-3 x^2-\sqrt {8 x^4+e^{4 c_1}}} \\ y(x)\to \sqrt {-3 x^2-\sqrt {8 x^4+e^{4 c_1}}} \\ y(x)\to -\sqrt {-3 x^2+\sqrt {8 x^4+e^{4 c_1}}} \\ y(x)\to \sqrt {-3 x^2+\sqrt {8 x^4+e^{4 c_1}}} \\ y(x)\to -\sqrt {-2 \sqrt {2} \sqrt {x^4}-3 x^2} \\ y(x)\to \sqrt {-2 \sqrt {2} \sqrt {x^4}-3 x^2} \\ y(x)\to -\sqrt {2 \sqrt {2} \sqrt {x^4}-3 x^2} \\ y(x)\to \sqrt {2 \sqrt {2} \sqrt {x^4}-3 x^2} \\ \end{align*}