Internal problem ID [3870]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 3
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, _dAlembert]
Solve \begin {gather*} \boxed {x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 119
dsolve((x^3+3*x*y(x)^2)+(y(x)^3+3*x^2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-3 c_{1} x^{2}-\sqrt {8 x^{4} c_{1}^{2}+1}}}{\sqrt {c_{1}}} \\ y \relax (x ) = \frac {\sqrt {-3 c_{1} x^{2}+\sqrt {8 x^{4} c_{1}^{2}+1}}}{\sqrt {c_{1}}} \\ y \relax (x ) = -\frac {\sqrt {-3 c_{1} x^{2}-\sqrt {8 x^{4} c_{1}^{2}+1}}}{\sqrt {c_{1}}} \\ y \relax (x ) = -\frac {\sqrt {-3 c_{1} x^{2}+\sqrt {8 x^{4} c_{1}^{2}+1}}}{\sqrt {c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 7.934 (sec). Leaf size: 245
DSolve[(x^3+3*x*y[x]^2)+(y[x]^3+3*x^2*y[x])*y'[x]==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*}