Internal problem ID [3306]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 564.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {x \left (x^{n}+a y\right ) y^{\prime }+\left (b +c y\right ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.132 (sec). Leaf size: 107
dsolve(x*(x^n+a*y(x))*diff(y(x),x)+(b+c*y(x))*y(x)^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {b}{\RootOf \left (-x^{-n} \textit {\_Z}^{\frac {a n}{b}} a^{2} b n -x^{-n} \textit {\_Z}^{\frac {a n}{b}} a \,b^{2}+c_{1} a^{2} n^{2}+\textit {\_Z}^{\frac {a n}{b}} a c n -\textit {\_Z}^{\frac {a n +b}{b}} a n b +c_{1} a b n +\textit {\_Z}^{\frac {a n}{b}} b c \right ) b -c} \]
✓ Solution by Mathematica
Time used: 1.489 (sec). Leaf size: 91
DSolve[x(x^n+a y[x])y'[x]+(b+c y[x])y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)^{-\frac {a n+b}{b}} (c y(x)-a n) (b+c y(x))^{\frac {a n}{b}}}{a^2 n^2 (a n+b)}-\frac {x^{-n} e^{-\frac {a n (\log (y(x))-\log (b+c y(x)))}{b}}}{a n^2}=c_1,y(x)\right ] \]