73.15.69 problem 22.13 (g)

Internal problem ID [15429]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.13 (g)
Date solved : Monday, March 31, 2025 at 01:37:21 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=5 x^{5} {\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 48

ode:=diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)+diff(y(x),x)-y(x) = 5*x^5*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (625 x^{5}-5625 x^{4}+28000 x^{3}-91200 x^{2}+187320 x -188376\right ) {\mathrm e}^{2 x}}{625}+c_1 \cos \left (x \right )+c_2 \,{\mathrm e}^{x}+c_3 \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 58

ode=D[y[x],{x,3}]-D[y[x],{x,2}]+D[y[x],x]-y[x]==5*x^5*Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (e^x \left (x^5-9 x^4+\frac {224 x^3}{5}-\frac {3648 x^2}{25}+\frac {37464 x}{125}-\frac {188376}{625}\right )+c_3\right )+c_1 \cos (x)+c_2 \sin (x) \]

✓ Sympy. Time used: 0.408 (sec). Leaf size: 53

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*x**5*exp(2*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)
 

\[ y{\left (x \right )} = C_{1} e^{x} + C_{2} \sin {\left (x \right )} + C_{3} \cos {\left (x \right )} + \left (x^{5} - 9 x^{4} + \frac {224 x^{3}}{5} - \frac {3648 x^{2}}{25} + \frac {37464 x}{125} - \frac {188376}{625}\right ) e^{2 x} \]