83.36.3 problem 3

Internal problem ID [19366]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (A) at page 125
Problem number : 3
Date solved : Monday, March 31, 2025 at 07:11:34 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 23

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

\[ y(x)\to e^x (c_2 \operatorname {ExpIntegralEi}(-x)+\log (-x)+c_1) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2)) + (1 - x)*Derivative(y(x), x) - y(x) - exp(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x*Derivative(y(x), (x, 2)) - y(x) - exp(x))/(x - 1) cannot be solved by the factorable group method