73.12.14 problem 19.3 (b)

Internal problem ID [15295]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.3 (b)
Date solved : Monday, March 31, 2025 at 01:33:36 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=13\\ y^{\prime \prime }\left (0\right )&=86 \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 19

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+12*diff(y(x),x)-8*y(x) = 0; 
ic:=y(0) = 5, D(y)(0) = 13, (D@@2)(y)(0) = 86; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \left (27 x^{2}+3 x +5\right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 21

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+12*D[y[x],x]-8*y[x]==0; 
ic={y[0]==5,Derivative[1][y][0] ==13,Derivative[2][y][0] ==86}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} \left (27 x^2+3 x+5\right ) \]

✓ Sympy. Time used: 0.230 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*y(x) + 12*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): 5, Subs(Derivative(y(x), x), x, 0): 13, Subs(Derivative(y(x), (x, 2)), x, 0): 86} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (x \left (27 x + 3\right ) + 5\right ) e^{2 x} \]