39.3.3 problem Problem 12.3

Internal problem ID [6529]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 12. VARIATION OF PARAMETERS. page 104
Problem number : Problem 12.3
Date solved : Sunday, March 30, 2025 at 11:06:34 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 22

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

\[ y(x)\to e^x (x \log (x)+(-1+c_2) x+c_1) \]

✓ Sympy. Time used: 0.231 (sec). Leaf size: 14

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

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