20.9.14 problem Problem 13

Internal problem ID [3758]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.7, The Variation of Parameters Method. page 556
Problem number : Problem 13
Date solved : Tuesday, March 04, 2025 at 05:13:06 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = 4*exp(x)/x^3*ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (c_{1} x^{2}+c_{2} x +2 \ln \left (x \right )+3\right )}{x} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 28

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

\[ y(x)\to \frac {e^x \left (c_2 x^2+2 \log (x)+c_1 x+3\right )}{x} \]

✓ Sympy. Time used: 0.276 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x + \frac {2 \log {\left (x \right )}}{x} + \frac {3}{x}\right ) e^{x} \]