Internal problem ID [3301]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 557.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {3 x \left (x +2 y\right ) y^{\prime }+x^{3}+3 y \left (2 x +y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 63
dsolve(3*x*(x+2*y(x))*diff(y(x),x)+x^3+3*y(x)*(2*x+y(x)) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-3 x^{2}+\sqrt {-3 x^{5}+9 x^{4}-12 c_{1} x}}{6 x} \\ y \relax (x ) = -\frac {3 x^{2}+\sqrt {-3 x^{5}+9 x^{4}-12 c_{1} x}}{6 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.445 (sec). Leaf size: 71
DSolve[3 x(x+2 y[x])y'[x]+x^3+3 y[x](2 x+y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3 x^2+\sqrt {-3 (x-3) x^4+36 c_1 x}}{6 x} \\ y(x)\to \frac {-3 x^2+\sqrt {-3 (x-3) x^4+36 c_1 x}}{6 x} \\ \end{align*}