56.27.7 problem Ex 7

Internal problem ID [14226]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 50. Method of undetermined coefficients. Page 107
Problem number : Ex 7
Date solved : Thursday, October 02, 2025 at 09:26:54 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=4+{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 38

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

\[ y = 4+\left (c_4 x +c_2 \right ) {\mathrm e}^{-x}+\frac {\left (3+2 x^{2}+4 \left (-1+4 c_3 \right ) x +16 c_1 \right ) {\mathrm e}^{x}}{16} \]

✓ Mathematica. Time used: 0.113 (sec). Leaf size: 47

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

\begin{align*} y(x)&\to e^x \left (\frac {x^2}{8}+\left (-\frac {1}{4}+c_4\right ) x+\frac {3}{16}+c_3\right )+e^{-x} ((2+c_2) x+c_1)+4 \end{align*}

✓ Sympy. Time used: 0.080 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{- x} + \left (C_{3} + x \left (C_{4} + \frac {x}{8}\right )\right ) e^{x} + 4 \]