75.20.2 problem 637

Internal problem ID [17065]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 637
Date solved : Monday, March 31, 2025 at 03:39:48 PM
CAS classification : [_Jacobi]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

\[ y = \frac {c_1}{x^{2}}+c_2 \left (x -\frac {3}{2}\right ) \]

✓ Mathematica. Time used: 0.241 (sec). Leaf size: 107

ode=(x^2-x)*D[y[x],{x,2}]+(2*x-3)*D[y[x],x]-2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

False