54.3.145 problem 1159

Internal problem ID [12440]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1159
Date solved : Wednesday, October 01, 2025 at 01:45:02 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y-a \,x^{2}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

\[ y = c_2 x +\frac {a \,x^{2}}{3}+\frac {c_1}{x} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \frac {a x^2}{3}+c_2 x+\frac {c_1}{x} \end{align*}

✓ Sympy. Time used: 0.150 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \frac {C_{1}}{x} + C_{2} x + \frac {a x^{2}}{3} \]