63.1.93 problem 140

Internal problem ID [15533]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 140
Date solved : Thursday, October 02, 2025 at 10:19:39 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-5*diff(diff(y(x),x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 35

ode=D[y[x],{x,4}]-5*D[y[x],{x,2}]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.044 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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