83.41.21 problem 5 (viii)

Internal problem ID [19430]
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 : 5 (viii)
Date solved : Monday, March 31, 2025 at 07:13:29 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-\left (4 x^{2}-3 x -5\right ) y^{\prime }+\left (4 x^{2}-6 x -5\right ) y&={\mathrm e}^{2 x} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 8

ode:=(x^2-1)*diff(diff(y(x),x),x)-(4*x^2-3*x-5)*diff(y(x),x)+(4*x^2-6*x-5)*y(x) = exp(2*x); 
ic:=y(0) = 1, D(y)(0) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.112 (sec). Leaf size: 10

ode=(x^2-1)*D[y[x],{x,2}]-(4*x^2-3*x-5)*D[y[x],x]+(4*x^2-6*x-5)*y[x]==Exp[2*x]; 
ic={y[0]==1,Derivative[1][y][0] == 2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x**2 - 1)*Derivative(y(x), (x, 2)) + (4*x**2 - 6*x - 5)*y(x) - (4*x**2 - 3*x - 5)*Derivative(y(x), x) - exp(2*x),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-4*x**2*y(x) - x**2*Derivative(y(x), (x, 2)) + 6*x*y(x) + 5*y(x) + exp(2*x) + Derivative(y(x), (x, 2)))/(-4*x**2 + 3*x + 5) cannot be solved by the factorable group method