63.1.99 problem 146

Internal problem ID [15539]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 146
Date solved : Thursday, October 02, 2025 at 10:19:41 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 53

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\left (\left (-c_4 \,{\mathrm e}^{\sqrt {2}\, x}-c_3 \right ) \cos \left (\frac {\sqrt {2}\, x}{2}\right )+\sin \left (\frac {\sqrt {2}\, x}{2}\right ) \left (c_2 \,{\mathrm e}^{\sqrt {2}\, x}+c_1 \right )\right ) {\mathrm e}^{-\frac {\sqrt {2}\, x}{2}} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 65

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

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

✓ Sympy. Time used: 0.091 (sec). Leaf size: 70

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

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