Internal problem ID [3813]
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`]]
\[ \boxed {x \left (x -y a \right ) y^{\prime }-y \left (y-a x \right )=0} \]
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 60
dsolve(x*(x-a*y(x))*diff(y(x),x) = y(x)*(y(x)-a*x),y(x), singsol=all)
\[ y \left (x \right ) = x^{-a} {\mathrm e}^{\left (-a +1\right ) \operatorname {RootOf}\left (x^{a +1} {\mathrm e}^{a \textit {\_Z} +c_{1} a +c_{1}}+x^{a +1} {\mathrm e}^{a \textit {\_Z} +c_{1} a -\textit {\_Z} +c_{1}}-1\right )-c_{1} \left (a +1\right )} \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 36
DSolve[x(x-a y[x])y'[x]==y[x](y[x]-a x),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [(a-1) \log \left (1-\frac {y(x)}{x}\right )+\log \left (\frac {y(x)}{x}\right )=-(a+1) \log (x)+c_1,y(x)\right ] \]