Internal problem ID [3389]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 650.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x \left (x^{2}+2 y^{2}\right ) y^{\prime }-\left (2 x^{2}+3 y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 89
dsolve(x*(x^2+2*y(x)^2)*diff(y(x),x) = (2*x^2+3*y(x)^2)*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-2-2 \sqrt {4 c_{1} x^{2}+1}}\, x}{2} \\ y \relax (x ) = \frac {\sqrt {-2-2 \sqrt {4 c_{1} x^{2}+1}}\, x}{2} \\ y \relax (x ) = -\frac {\sqrt {-2+2 \sqrt {4 c_{1} x^{2}+1}}\, x}{2} \\ y \relax (x ) = \frac {\sqrt {-2+2 \sqrt {4 c_{1} x^{2}+1}}\, x}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 40.704 (sec). Leaf size: 277
DSolve[x(x^2+2 y[x]^2)y'[x]==(2 x^2+3 y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x^2-\sqrt {x^4+4 e^{2 c_1} x^6}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-x^2-\sqrt {x^4+4 e^{2 c_1} x^6}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-x^2+\sqrt {x^4+4 e^{2 c_1} x^6}}}{\sqrt {2}} \\ y(x)\to \sqrt {-\frac {x^2}{2}+\frac {1}{2} \sqrt {x^4+4 e^{2 c_1} x^6}} \\ y(x)\to -\frac {\sqrt {-\sqrt {x^4}-x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-\sqrt {x^4}-x^2}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {\sqrt {x^4}-x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {\sqrt {x^4}-x^2}}{\sqrt {2}} \\ \end{align*}