7.9.4 problem 16

Internal problem ID [252]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.2 (General solutions of linear equations). Problems at page 122
Problem number : 16
Date solved : Tuesday, March 04, 2025 at 11:06:22 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+8 y^{\prime }-4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=4\\ y^{\prime \prime }\left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 19

ode:=diff(diff(diff(y(x),x),x),x)-5*diff(diff(y(x),x),x)+8*diff(y(x),x)-4*y(x) = 0; 
ic:=y(0) = 1, D(y)(0) = 4, (D@@2)(y)(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \left (-10 x +13\right ) {\mathrm e}^{2 x}-12 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 21

ode=D[y[x],{x,3}]-5*D[y[x],{x,2}]+8*D[y[x],x]-4*y[x]==0; 
ic={y[0]==1,Derivative[1][y][0] ==4,Derivative[2][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -e^x \left (e^x (10 x-13)+12\right ) \]

✓ Sympy. Time used: 0.213 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) + 8*Derivative(y(x), x) - 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 4, Subs(Derivative(y(x), (x, 2)), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (\left (13 - 10 x\right ) e^{x} - 12\right ) e^{x} \]