69.1.97 problem 144

Internal problem ID [14171]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 144
Date solved : Wednesday, March 05, 2025 at 10:37:30 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 41

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(y(x),x),x)+9*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 52

ode=D[y[x],{x,4}]+2*D[y[x],{x,2}]+9*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.129 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) + 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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