Internal problem ID [3387]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 648.
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 +y^{2}\right ) y^{\prime }-\left (x^{2}+b x y+y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 43
dsolve(x*(x^2+a*x*y(x)+y(x)^2)*diff(y(x),x) = (x^2+b*x*y(x)+y(x)^2)*y(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left ({\mathrm e}^{\textit {\_Z}} a \ln \relax (x )-\ln \relax (x ) {\mathrm e}^{\textit {\_Z}} b +{\mathrm e}^{\textit {\_Z}} c_{1} a -c_{1} b \,{\mathrm e}^{\textit {\_Z}}+\textit {\_Z} a \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{2 \textit {\_Z}}-1\right )} x \]
✓ Solution by Mathematica
Time used: 0.238 (sec). Leaf size: 38
DSolve[x(x^2+a x y[x]+y[x]^2)y'[x]==(x^2+b x y[x]+y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [a \log \left (\frac {y(x)}{x}\right )-\frac {x}{y(x)}+\frac {y(x)}{x}=(b-a) \log (x)+c_1,y(x)\right ] \]