69.1.100 problem 147

Internal problem ID [14174]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 147
Date solved : Wednesday, March 05, 2025 at 10:37:32 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-a^{4} y&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 30

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-a^4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} {\mathrm e}^{a x}+c_{2} {\mathrm e}^{-a x}+c_{3} \sin \left (a x \right )+c_4 \cos \left (a x \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 37

ode=D[y[x],{x,4}]-a^4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 e^{-a x}+c_4 e^{a x}+c_1 \cos (a x)+c_3 \sin (a x) \]

✓ Sympy. Time used: 0.134 (sec). Leaf size: 32

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

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