32.9.14 problem Exercise 22.14, page 240

Internal problem ID [5988]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number : Exercise 22.14, page 240
Date solved : Wednesday, March 05, 2025 at 12:01:58 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

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

\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (2 \ln \left (x \right ) x^{2}+4 c_{1} x -3 x^{2}+4 c_{2} \right )}{4} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{4} e^x \left (-3 x^2+2 x^2 \log (x)+4 c_2 x+4 c_1\right ) \]

✓ Sympy. Time used: 0.264 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} + \frac {x \log {\left (x \right )}}{2} - \frac {3 x}{4}\right )\right ) e^{x} \]