Internal problem ID [3296]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 552.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _exact, _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 50
dsolve(2*x*(2*x^2+y(x))*diff(y(x),x)+(12*x^2+y(x))*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-2 x^{3}+\sqrt {4 x^{6}+c_{1} x}}{x} \\ y \relax (x ) = -\frac {2 x^{3}+\sqrt {4 x^{6}+c_{1} x}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.428 (sec). Leaf size: 58
DSolve[2 x(2 x^2+y[x])y'[x]+(12 x^2+y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 x^3+\sqrt {x \left (4 x^5+c_1\right )}}{x} \\ y(x)\to \frac {-2 x^3+\sqrt {x \left (4 x^5+c_1\right )}}{x} \\ \end{align*}