15.9.20 problem 34

Internal problem ID [3077]
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 : 34
Date solved : Sunday, March 30, 2025 at 01:18:03 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-20 y^{\prime \prime }+27 y^{\prime }+18 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

ode:=2*diff(diff(diff(diff(y(x),x),x),x),x)-3*diff(diff(diff(y(x),x),x),x)-20*diff(diff(y(x),x),x)+27*diff(y(x),x)+18*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 40

ode=2*D[y[x],{x,4}]-3*D[y[x],{x,3}]-20*D[y[x],{x,2}]+27*D[y[x],x]+18*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x} \left (c_1 e^{5 x/2}+c_3 e^{5 x}+c_4 e^{6 x}+c_2\right ) \]

✓ Sympy. Time used: 0.210 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(18*y(x) + 27*Derivative(y(x), x) - 20*Derivative(y(x), (x, 2)) - 3*Derivative(y(x), (x, 3)) + 2*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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