Internal problem ID [8480]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 144.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {x^{2} \left (y^{\prime }+a y^{2}\right )=-b \,x^{\alpha }-c} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 219
dsolve(x^2*(diff(y(x),x)+a*y(x)^2) + b*x^alpha + c=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-2 \sqrt {a b}\, \left (\operatorname {BesselY}\left (\frac {\sqrt {-4 a c +1}}{\alpha }+1, \frac {2 \sqrt {a b}\, x^{\frac {\alpha }{2}}}{\alpha }\right ) c_{1} +\operatorname {BesselJ}\left (\frac {\sqrt {-4 a c +1}}{\alpha }+1, \frac {2 \sqrt {a b}\, x^{\frac {\alpha }{2}}}{\alpha }\right )\right ) x^{\frac {\alpha }{2}}+\left (\sqrt {-4 a c +1}+1\right ) \left (\operatorname {BesselY}\left (\frac {\sqrt {-4 a c +1}}{\alpha }, \frac {2 \sqrt {a b}\, x^{\frac {\alpha }{2}}}{\alpha }\right ) c_{1} +\operatorname {BesselJ}\left (\frac {\sqrt {-4 a c +1}}{\alpha }, \frac {2 \sqrt {a b}\, x^{\frac {\alpha }{2}}}{\alpha }\right )\right )}{2 x a \left (\operatorname {BesselY}\left (\frac {\sqrt {-4 a c +1}}{\alpha }, \frac {2 \sqrt {a b}\, x^{\frac {\alpha }{2}}}{\alpha }\right ) c_{1} +\operatorname {BesselJ}\left (\frac {\sqrt {-4 a c +1}}{\alpha }, \frac {2 \sqrt {a b}\, x^{\frac {\alpha }{2}}}{\alpha }\right )\right )} \]
✓ Solution by Mathematica
Time used: 1.108 (sec). Leaf size: 1777
DSolve[x^2*(y'[x]+a*y[x]^2) + b*x^\[Alpha] + c==0,y[x],x,IncludeSingularSolutions -> True]
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