75.16.23 problem 496

Internal problem ID [16917]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 496
Date solved : Thursday, March 13, 2025 at 09:00:25 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=3 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-diff(diff(y(x),x),x) = 3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} c_{2} -\frac {3 x^{2}}{2}+c_{1} {\mathrm e}^{-x}+c_{3} x +c_4 \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 33

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

\[ y(x)\to -\frac {3 x^2}{2}+c_4 x+c_1 e^x+c_2 e^{-x}+c_3 \]

✓ Sympy. Time used: 0.099 (sec). Leaf size: 24

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

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