6.19.17 problem section 9.3, problem 17

Internal problem ID [2164]
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 17
Date solved : Tuesday, September 30, 2025 at 05:24:31 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \left (x^{2}+4 x +3\right ) \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 101

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-2*diff(diff(diff(y(x),x),x),x)+3*diff(y(x),x)-y(x) = exp(x)*(x^2+4*x+3); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+3 \textit {\_Z} -1, \operatorname {index} =1\right ) x}+c_2 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+3 \textit {\_Z} -1, \operatorname {index} =2\right ) x}+c_3 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+3 \textit {\_Z} -1, \operatorname {index} =3\right ) x}+c_4 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+3 \textit {\_Z} -1, \operatorname {index} =4\right ) x}+\left (x +1\right )^{2} {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 123

ode=D[y[x],{x,4}]-2*D[y[x],{x,3}]+0*D[y[x],{x,2}]+3*D[y[x],x]-y[x]==Exp[x]*(3+4*x+x^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^4-2 \text {$\#$1}^3+3 \text {$\#$1}-1\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^4-2 \text {$\#$1}^3+3 \text {$\#$1}-1\&,3\right ]\right )+c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^4-2 \text {$\#$1}^3+3 \text {$\#$1}-1\&,4\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^4-2 \text {$\#$1}^3+3 \text {$\#$1}-1\&,1\right ]\right )+e^x (x+1)^2 \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -x**2*exp(x)/3 - 4*x*exp(x)/3 - y(x)/3 - exp(x) + Derivative(y(x), x) - 2*Derivative(y(x), (x, 3))/3 + Derivative(y(x), (x, 4))/3 cannot be solved by the factorable group method