88.19.5 problem 5

Internal problem ID [24133]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 139
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:00:06 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 37

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

\[ y = \frac {\left (\left (-5 x -8\right ) \cos \left (x \right )+\left (-10 x +19\right ) \sin \left (x \right )+25 c_2 \right ) {\mathrm e}^{x}}{25}+c_1 \cos \left (x \right )+c_3 \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 46

ode=D[y[x],{x,3}]-D[y[x],{x,2}]+D[y[x],x]-y[x]==x*Exp[x]*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3 e^x-\frac {1}{25} e^x ((10 x-19) \sin (x)+(5 x+8) \cos (x))+c_1 \cos (x)+c_2 \sin (x) \end{align*}

✓ Sympy. Time used: 0.186 (sec). Leaf size: 39

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

\[ y{\left (x \right )} = C_{2} \sin {\left (x \right )} + C_{3} \cos {\left (x \right )} + \left (C_{1} + \frac {\left (19 - 10 x\right ) \sin {\left (x \right )}}{25} + \frac {\left (- 5 x - 8\right ) \cos {\left (x \right )}}{25}\right ) e^{x} \]