69.1.96 problem 143

Internal problem ID [14170]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 143
Date solved : Wednesday, March 05, 2025 at 10:37:30 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-4 y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

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

\[ y = c_{1} +c_{2} x +c_{3} x^{2}+c_4 \,{\mathrm e}^{2 x}+c_5 \,{\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 39

ode=D[y[x],{x,5}]-4*D[y[x],{x,3}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{8} c_1 e^{2 x}-\frac {1}{8} c_2 e^{-2 x}+x (c_5 x+c_4)+c_3 \]

✓ Sympy. Time used: 0.113 (sec). Leaf size: 26

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

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