54.3.184 problem 1198

Internal problem ID [12479]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1198
Date solved : Wednesday, October 01, 2025 at 01:45:37 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (3 x +2\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

ode:=x^2*diff(diff(y(x),x),x)-(x^2-2*x)*diff(y(x),x)-(2+3*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {Ei}_{1}\left (x \right ) {\mathrm e}^{x} c_2 \,x^{3}+c_1 \,x^{3} {\mathrm e}^{x}-c_2 \left (x^{2}-x +2\right )}{x^{2}} \]

✓ Mathematica. Time used: 0.162 (sec). Leaf size: 34

ode=(-2 - 3*x)*y[x] - (-2*x + x^2)*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 e^x x \left (c_2 \int _1^x\frac {e^{-K[1]}}{K[1]^4}dK[1]+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - (3*x + 2)*y(x) - (x**2 - 2*x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False