15.9.25 problem 39

Internal problem ID [3082]
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 : 39
Date solved : Sunday, March 30, 2025 at 01:18:08 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-7 y^{\prime \prime }-8 y^{\prime }+12 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(diff(y(x),x),x),x)-7*diff(diff(y(x),x),x)-8*diff(y(x),x)+12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 35

ode=D[y[x],{x,4}]+2*D[y[x],{x,3}]-7*D[y[x],{x,2}]-8*D[y[x],x]+12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.211 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*y(x) - 8*Derivative(y(x), x) - 7*Derivative(y(x), (x, 2)) + 2*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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