83.27.8 problem 8

Internal problem ID [19283]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (A) at page 104
Problem number : 8
Date solved : Monday, March 31, 2025 at 07:05:33 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-4 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 58

ode:=(x^2-x)*diff(diff(y(x),x),x)-2*(x-1)*diff(y(x),x)-4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -4 c_1 \,x^{3} \left (x -1\right ) \ln \left (x -1\right )+4 c_1 \,x^{3} \left (x -1\right ) \ln \left (x \right )+c_2 \,x^{4}+\left (-4 c_1 -c_2 \right ) x^{3}+2 c_1 \,x^{2}+\frac {2 c_1 x}{3}+\frac {c_1}{3} \]

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 61

ode=(x^2-x)*D[y[x],{x,2}]-2*(x-1)*D[y[x],x]-4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{3} c_2 \left (12 x^3+12 (x-1) x^3 \log (1-x)-12 (x-1) x^3 \log (x)-6 x^2-2 x-1\right )-c_1 (x-1) x^3 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2 - 2*x)*Derivative(y(x), x) + (x**2 - x)*Derivative(y(x), (x, 2)) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False