15.9.28 problem 42

Internal problem ID [3085]
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 : 42
Date solved : Sunday, March 30, 2025 at 01:18:11 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-15 y^{\prime \prime \prime }-19 y^{\prime \prime }+30 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)+3*diff(diff(diff(diff(y(x),x),x),x),x)-15*diff(diff(diff(y(x),x),x),x)-19*diff(diff(y(x),x),x)+30*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 47

ode=D[y[x],{x,5}]+3*D[y[x],{x,4}]-15*D[y[x],{x,3}]-19*D[y[x],{x,2}]+30*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {1}{5} c_1 e^{-5 x}-\frac {1}{2} c_2 e^{-2 x}+c_3 e^x+\frac {1}{3} c_4 e^{3 x}+c_5 \]

✓ Sympy. Time used: 0.232 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(30*Derivative(y(x), x) - 19*Derivative(y(x), (x, 2)) - 15*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)
 

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