Internal problem ID [3928]
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]
\[ \boxed {\left (y^{2}+3 x^{2}\right ) y y^{\prime }+x \left (3 y^{2}+x^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) = \frac {\sqrt {-3 c_{1} x^{2}-\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} y \left (x \right ) = \frac {\sqrt {-3 c_{1} x^{2}+\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} y \left (x \right ) = -\frac {\sqrt {-3 c_{1} x^{2}-\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} y \left (x \right ) = -\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: 8.329 (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*}