Internal problem ID [3391]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 652.
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}+a y x +2 y^{2}\right ) y^{\prime }-\left (a x +2 y\right ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 21
dsolve(x*(x^2+a*x*y(x)+2*y(x)^2)*diff(y(x),x) = (a*x+2*y(x))*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left ({\mathrm e}^{2 \textit {\_Z}}+a \,{\mathrm e}^{\textit {\_Z}}+c_{1}+\textit {\_Z} +\ln \relax (x )\right )} x \]
✓ Solution by Mathematica
Time used: 0.164 (sec). Leaf size: 34
DSolve[x(x^2+a x y[x]+2 y[x]^2)y'[x]==(a x+2 y[x])y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {a y(x)}{x}+\frac {y(x)^2}{x^2}+\log \left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]