58.11.10 problem 10

Internal problem ID [14741]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:50:41 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y&=8 x \,{\mathrm e}^{-2 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 32

ode:=diff(diff(diff(y(x),x),x),x)+2*diff(diff(y(x),x),x)-3*diff(y(x),x)-10*y(x) = 8*x*exp(-2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (2 c_1 \,{\mathrm e}^{4 x}+2 c_3 \sin \left (x \right )+2 c_2 \cos \left (x \right )-4 x -1\right ) {\mathrm e}^{-2 x}}{2} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 40

ode=D[y[x],{x,3}]+2*D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==8*x*Exp[-2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} e^{-2 x} \left (-4 x+2 c_3 e^{4 x}+2 c_2 \cos (x)+2 c_1 \sin (x)-1\right ) \end{align*}

✓ Sympy. Time used: 0.254 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x*exp(-2*x) - 10*y(x) - 3*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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