67.2.4 problem Problem 1(d)

Internal problem ID [13890]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 1(d)
Date solved : Monday, March 31, 2025 at 08:16:33 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime }&=2 x^{2}+3 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 372

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 182

ode=D[y[x],{x,5}]-D[y[x],{x,4}] +D[y[x],x]==2*x^2+3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,2\right ]\right )}{\text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,2\right ]}+\frac {c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,1\right ]\right )}{\text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,1\right ]}+\frac {c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,4\right ]\right )}{\text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,4\right ]}+\frac {c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,3\right ]\right )}{\text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,3\right ]}+\frac {2 x^3}{3}+3 x+c_5 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x**2 + Derivative(y(x), x) - Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 5)) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : Cannot find 5 solutions to the homogeneous equation necessary to apply undetermined coefficients to -2*x**2 + Derivative(y(x), x) - Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 5)) - 3 (number of terms != order)