60.1.143 problem 144

Internal problem ID [10157]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 144
Date solved : Monday, January 27, 2025 at 06:30:22 PM
CAS classification : [_rational, _Riccati]

\begin{align*} x^{2} \left (y^{\prime }+a y^{2}\right )+b \,x^{\alpha }+c&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 219

dsolve(x^2*(diff(y(x),x)+a*y(x)^2) + b*x^alpha + c=0,y(x), singsol=all)
 

\[ y = \frac {-2 \sqrt {a b}\, \left (\operatorname {BesselY}\left (\frac {\sqrt {-4 a c +1}}{\alpha }+1, \frac {2 \sqrt {a b}\, x^{\frac {\alpha }{2}}}{\alpha }\right ) c_{1} +\operatorname {BesselJ}\left (\frac {\sqrt {-4 a c +1}}{\alpha }+1, \frac {2 \sqrt {a b}\, x^{\frac {\alpha }{2}}}{\alpha }\right )\right ) x^{\frac {\alpha }{2}}+\left (\sqrt {-4 a c +1}+1\right ) \left (\operatorname {BesselY}\left (\frac {\sqrt {-4 a c +1}}{\alpha }, \frac {2 \sqrt {a b}\, x^{\frac {\alpha }{2}}}{\alpha }\right ) c_{1} +\operatorname {BesselJ}\left (\frac {\sqrt {-4 a c +1}}{\alpha }, \frac {2 \sqrt {a b}\, x^{\frac {\alpha }{2}}}{\alpha }\right )\right )}{2 x a \left (\operatorname {BesselY}\left (\frac {\sqrt {-4 a c +1}}{\alpha }, \frac {2 \sqrt {a b}\, x^{\frac {\alpha }{2}}}{\alpha }\right ) c_{1} +\operatorname {BesselJ}\left (\frac {\sqrt {-4 a c +1}}{\alpha }, \frac {2 \sqrt {a b}\, x^{\frac {\alpha }{2}}}{\alpha }\right )\right )} \]

✓ Solution by Mathematica

Time used: 1.011 (sec). Leaf size: 1777

DSolve[x^2*(D[y[x],x]+a*y[x]^2) + b*x^\[Alpha] + c==0,y[x],x,IncludeSingularSolutions -> True]
 

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