Internal problem ID [3425]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 686.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (5 x^{2}+2 y^{2}\right ) y y^{\prime }+x \left (x^{2}+5 y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 125
dsolve((5*x^2+2*y(x)^2)*y(x)*diff(y(x),x)+x*(x^2+5*y(x)^2) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-10 c_{1} x^{2}-2 \sqrt {23 x^{4} c_{1}^{2}+2}}}{2 \sqrt {c_{1}}} \\ y \relax (x ) = \frac {\sqrt {-10 c_{1} x^{2}-2 \sqrt {23 x^{4} c_{1}^{2}+2}}}{2 \sqrt {c_{1}}} \\ y \relax (x ) = -\frac {\sqrt {-10 c_{1} x^{2}+2 \sqrt {23 x^{4} c_{1}^{2}+2}}}{2 \sqrt {c_{1}}} \\ y \relax (x ) = \frac {\sqrt {-10 c_{1} x^{2}+2 \sqrt {23 x^{4} c_{1}^{2}+2}}}{2 \sqrt {c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 20.764 (sec). Leaf size: 295
DSolve[(5 x^2+2 y[x]^2)y[x] y'[x]+x(x^2+5 y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ \end{align*}