64.10.44 problem 46

Internal problem ID [13371]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 46
Date solved : Wednesday, March 05, 2025 at 09:49:19 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }+13 y^{\prime }+30 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 35

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+3*diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)+13*diff(y(x),x)+30*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_4 \,{\mathrm e}^{4 x} \cos \left (2 x \right )+c_{3} {\mathrm e}^{4 x} \sin \left (2 x \right )+{\mathrm e}^{x} c_{2} +c_{1} \right ) {\mathrm e}^{-3 x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 43

ode=D[y[x],{x,4}]+3*D[y[x],{x,3}]+D[y[x],{x,2}]+13*D[y[x],x]+30*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 e^x \cos (2 x)+e^{-3 x} \left (c_4 e^x+c_1 e^{4 x} \sin (2 x)+c_3\right ) \]

✓ Sympy. Time used: 0.258 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(30*y(x) + 13*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + 3*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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