Internal problem ID [7723]
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]
\[ \boxed {x^{2} \left (y^{\prime }+a y^{2}\right )+b \,x^{\alpha }+c=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 244
dsolve(x^2*(diff(y(x),x)+a*y(x)^2) + b*x^alpha + c=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (-\sqrt {-4 a c +1}\, c_{1} -c_{1} \right ) \operatorname {BesselY}\left (\frac {\sqrt {-4 a c +1}}{\alpha }, \frac {2 \sqrt {b a}\, x^{\frac {\alpha }{2}}}{\alpha }\right )+2 x^{\frac {\alpha }{2}} \operatorname {BesselY}\left (\frac {\sqrt {-4 a c +1}+\alpha }{\alpha }, \frac {2 \sqrt {b a}\, x^{\frac {\alpha }{2}}}{\alpha }\right ) \sqrt {b a}\, c_{1} +\left (-\sqrt {-4 a c +1}-1\right ) \operatorname {BesselJ}\left (\frac {\sqrt {-4 a c +1}}{\alpha }, \frac {2 \sqrt {b a}\, x^{\frac {\alpha }{2}}}{\alpha }\right )+2 \operatorname {BesselJ}\left (\frac {\sqrt {-4 a c +1}+\alpha }{\alpha }, \frac {2 \sqrt {b a}\, x^{\frac {\alpha }{2}}}{\alpha }\right ) \sqrt {b a}\, x^{\frac {\alpha }{2}}}{2 x a \left (\operatorname {BesselY}\left (\frac {\sqrt {-4 a c +1}}{\alpha }, \frac {2 \sqrt {b a}\, x^{\frac {\alpha }{2}}}{\alpha }\right ) c_{1} +\operatorname {BesselJ}\left (\frac {\sqrt {-4 a c +1}}{\alpha }, \frac {2 \sqrt {b a}\, x^{\frac {\alpha }{2}}}{\alpha }\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.93 (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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