Internal problem ID [3305]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 561.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (x -a y\right ) y^{\prime }-y \left (y-a x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.056 (sec). Leaf size: 95
dsolve(x*(x-a*y(x))*diff(y(x),x) = y(x)*(y(x)-a*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-c_{1} a -a \ln \relax (x )-\RootOf \left (x \,{\mathrm e}^{c_{1} a} x^{a} {\mathrm e}^{a \textit {\_Z}} {\mathrm e}^{c_{1}}+{\mathrm e}^{c_{1} a} x^{a} {\mathrm e}^{a \textit {\_Z}} {\mathrm e}^{c_{1}} {\mathrm e}^{-\textit {\_Z}} x -1\right ) a -c_{1}+\RootOf \left (x \,{\mathrm e}^{c_{1} a} x^{a} {\mathrm e}^{a \textit {\_Z}} {\mathrm e}^{c_{1}}+{\mathrm e}^{c_{1} a} x^{a} {\mathrm e}^{a \textit {\_Z}} {\mathrm e}^{c_{1}} {\mathrm e}^{-\textit {\_Z}} x -1\right )} \]
✓ Solution by Mathematica
Time used: 0.158 (sec). Leaf size: 36
DSolve[x(x-a y[x])y'[x]==y[x](y[x]-a x),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [(a-1) \log \left (1-\frac {y(x)}{x}\right )+\log \left (\frac {y(x)}{x}\right )=-(a+1) \log (x)+c_1,y(x)\right ] \]