54.3.238 problem 1254

Internal problem ID [12533]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1254
Date solved : Wednesday, October 01, 2025 at 01:57:14 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 43

ode:=(x^2+x-2)*diff(diff(y(x),x),x)+(x^2-x)*diff(y(x),x)-(6*x^2+7*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 195 c_2 \,{\mathrm e}^{-5+2 x} \left (x -1\right ) \operatorname {Ei}_{1}\left (5 x -5\right )-c_2 \left (x +44\right ) {\mathrm e}^{-3 x}+c_1 \,{\mathrm e}^{2 x} \left (x -1\right ) \]

✓ Mathematica. Time used: 0.143 (sec). Leaf size: 97

ode=(-7*x - 6*x^2)*y[x] + (-x + x^2)*D[y[x],x] + (-2 + x + x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x\left (-\frac {1}{K[1]+2}+\frac {5}{2}+\frac {1}{K[1]-1}\right )dK[1]-\frac {1}{2} \int _1^x\frac {K[2]}{K[2]+2}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\left (-\frac {1}{K[1]+2}+\frac {5}{2}+\frac {1}{K[1]-1}\right )dK[1]\right )dK[3]+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x**2 - x)*Derivative(y(x), x) - (6*x**2 + 7*x)*y(x) + (x**2 + x - 2)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False