7.9.6 problem 18

Internal problem ID [254]
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 : 18
Date solved : Tuesday, March 04, 2025 at 11:06:23 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 14

ode:=diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+4*diff(y(x),x)-2*y(x) = 0; 
ic:=y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -{\mathrm e}^{x} \left (-2+\sin \left (x \right )+\cos \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 16

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

\[ y(x)\to -e^x (\sin (x)+\cos (x)-2) \]

✓ Sympy. Time used: 0.204 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \left (- \sin {\left (x \right )} - \cos {\left (x \right )} + 2\right ) e^{x} \]