77.26.9 problem 9

Internal problem ID [20618]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 9
Date solved : Thursday, October 02, 2025 at 06:16:17 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&={\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

ode:=x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+2*y(x) = exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 +c_1 x +{\mathrm e}^{x}}{x^{2}} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 19

ode=x^2*D[y[x],{x,2}]+4*x*D[y[x],x]+2*y[x]==Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^x+c_2 x+c_1}{x^2} \end{align*}

✓ Sympy. Time used: 0.307 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \frac {C_{1} + C_{2} x + e^{x}}{x^{2}} \]