60.1.141 problem 144

Internal problem ID [10155]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 144
Date solved : Wednesday, March 05, 2025 at 08:34:00 AM
CAS classification : [_rational, _Riccati]

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

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

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

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

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

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

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
Alpha = symbols("Alpha") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
y = Function("y") 
ode = Eq(b*x**Alpha + c + x**2*(a*y(x)**2 + Derivative(y(x), x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-a*x**2*y(x)**2 - b*x**Alpha - c)/x**2 cannot be solved by the factorable group method