12.18.21 problem section 9.2, problem 21

Internal problem ID [2135]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 21
Date solved : Tuesday, March 04, 2025 at 01:50:41 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime }-11 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=13 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 21

ode:=2*diff(diff(diff(y(x),x),x),x)-11*diff(diff(y(x),x),x)+12*diff(y(x),x)+9*y(x) = 0; 
ic:=y(0) = 6, D(y)(0) = 3, (D@@2)(y)(0) = 13; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 25

ode=2*D[y[x],{x,3}]-11*D[y[x],{x,2}]+12*D[y[x],x]+9*y[x]==0; 
ic={y[0]==6,Derivative[1][y][0] ==3,Derivative[2][y][0] ==13}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 4 e^{-x/2}-e^{3 x} (x-2) \]

✓ Sympy. Time used: 0.261 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) + 12*Derivative(y(x), x) - 11*Derivative(y(x), (x, 2)) + 2*Derivative(y(x), (x, 3)),0) 
ics = {y(0): 6, Subs(Derivative(y(x), x), x, 0): 3, Subs(Derivative(y(x), (x, 2)), x, 0): 13} 
dsolve(ode,func=y(x),ics=ics)
 

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