15.9.26 problem 40

Internal problem ID [3083]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 40
Date solved : Sunday, March 30, 2025 at 01:18:09 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 33

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-3*diff(diff(diff(diff(y(x),x),x),x),x)-5*diff(diff(diff(y(x),x),x),x)+15*diff(diff(y(x),x),x)+4*diff(y(x),x)-12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_4 \,{\mathrm e}^{5 x}+c_1 \,{\mathrm e}^{4 x}+c_5 \,{\mathrm e}^{3 x}+c_3 \,{\mathrm e}^{x}+c_2 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 42

ode=D[y[x],{x,5}]-3*D[y[x],{x,4}]-5*D[y[x],{x,3}]+15*D[y[x],{x,2}]+4*D[y[x],x]-12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (c_2 e^x+e^{3 x} \left (e^x \left (c_5 e^x+c_4\right )+c_3\right )+c_1\right ) \]

✓ Sympy. Time used: 0.219 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*y(x) + 4*Derivative(y(x), x) + 15*Derivative(y(x), (x, 2)) - 5*Derivative(y(x), (x, 3)) - 3*Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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