83.41.9 problem 2 (viii)

Internal problem ID [19410]
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 at end of chapter VIII. Page 141
Problem number : 2 (viii)
Date solved : Thursday, March 13, 2025 at 02:24:18 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (2 x -1\right ) y^{\prime \prime }-2 y^{\prime }+\left (3-2 x \right ) y&=2 \,{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 45

ode:=(2*x-1)*diff(diff(y(x),x),x)-2*diff(y(x),x)+(3-2*x)*y(x) = 2*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = c_{2} {\mathrm e}^{x}+x \,{\mathrm e}^{-x} c_{1} +x \,\operatorname {Ei}_{1}\left (1-2 x \right ) {\mathrm e}^{1-x}+\frac {{\mathrm e}^{x} \ln \left (2 x -1\right )}{2}+\frac {{\mathrm e}^{x}}{2} \]

✓ Mathematica. Time used: 2.451 (sec). Leaf size: 97

ode=(2*x-1)*D[y[x],{x,2}]-2*D[y[x],x]+(3-2*x)*y[x]==2*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} e^{-x} \left (-2 e x \operatorname {ExpIntegralEi}(2 x-1)+e^{2 x}+e^{2 x} \log (1-2 x)+\frac {2 c_1 e^{2 x-\frac {1}{2}} \sqrt {1-2 x}}{\sqrt {2 x-1}}-\frac {2 c_2 x \sqrt {e-2 e x}}{\sqrt {2 x-1}}\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((3 - 2*x)*y(x) + (2*x - 1)*Derivative(y(x), (x, 2)) - 2*exp(x) - 2*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE x*y(x) - x*Derivative(y(x), (x, 2)) - 3*y(x)/2 + exp(x) + Derivative(y(x), x) + Derivative(y(x), (x, 2))/2 cannot be solved by the factorable group method