23.3.300 problem 302

Internal problem ID [6014]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 302
Date solved : Tuesday, September 30, 2025 at 02:19:53 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 19

ode=2*y[x] + 4*x*D[y[x],x] + x^2*D[y[x],{x,2}] == E^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)
 

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