7.11.22 problem 22

Internal problem ID [343]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 22
Date solved : Saturday, March 29, 2025 at 04:51:13 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 44

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

\[ y = -{\mathrm e}^{-x} c_2 +\frac {\left (-7+2 x +4 c_1 \right ) {\mathrm e}^{x}}{4}-\frac {x^{5}}{30}+\frac {x^{3}}{6}+\frac {c_3 \,x^{2}}{2}+c_4 x +c_5 \]

✓ Mathematica. Time used: 0.452 (sec). Leaf size: 56

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

\[ y(x)\to -\frac {x^5}{30}+\frac {x^3}{6}+c_5 x^2+c_4 x+e^x \left (\frac {x}{2}-\frac {7}{4}+c_1\right )-c_2 e^{-x}+c_3 \]

✓ Sympy. Time used: 0.165 (sec). Leaf size: 37

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

\[ y{\left (x \right )} = C_{1} + C_{2} x^{2} + C_{4} e^{- x} + C_{5} e^{x} - \frac {x^{5}}{30} + \frac {x^{3}}{6} + x \left (C_{3} + \frac {e^{x}}{2}\right ) \]