6.19.51 problem section 9.3, problem 51

Internal problem ID [2198]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 51
Date solved : Tuesday, September 30, 2025 at 05:24:54 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y&=10 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} \sin \left (2 x \right )-10 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 45

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)+9*diff(y(x),x)-10*y(x) = 10*exp(2*x)+20*exp(x)*sin(2*x)-10; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 1+{\mathrm e}^{x} \left (x +c_2 -\frac {8}{5}\right ) \cos \left (2 x \right )+\frac {\left (-4+10 x +5 c_1 \right ) {\mathrm e}^{2 x}}{5}-2 \left (x -\frac {c_3}{2}+\frac {13}{20}\right ) {\mathrm e}^{x} \sin \left (2 x \right ) \]

✓ Mathematica. Time used: 0.549 (sec). Leaf size: 72

ode=1*D[y[x],{x,3}]-4*D[y[x],{x,2}]+9*D[y[x],x]-10*y[x]==10*Exp[2*x]+20*Exp[x]*Sin[2*x]-10; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 e^{2 x} x-\frac {4 e^{2 x}}{5}+c_3 e^{2 x}+\frac {1}{10} e^x (10 x-11+10 c_2) \cos (2 x)-\frac {1}{20} e^x (40 x+21-20 c_1) \sin (2 x)+1 \end{align*}

✓ Sympy. Time used: 0.268 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-10*y(x) - 10*exp(2*x) - 20*exp(x)*sin(2*x) + 9*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) + 10,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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