83.27.7 problem 7

Internal problem ID [19282]
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 : 7
Date solved : Monday, March 31, 2025 at 07:05:32 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 41

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

\[ y = \frac {12 \ln \left (x \right ) c_1 \,x^{3}+\left (-3 x^{4}+18 x^{2}-6 x +1\right ) c_1 +c_2 \,x^{3}}{\left (x -1\right )^{5}} \]

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 52

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

\[ y(x)\to \frac {-3 c_2 x^4-3 c_1 x^3+12 c_2 x^3 \log (x)+18 c_2 x^2-6 c_2 x+c_2}{3 (x-1)^5} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((4*x + 2)*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