73.11.21 problem 17.4 (c)

Internal problem ID [15264]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 17. Second order Homogeneous equations with constant coefficients. Additional exercises page 334
Problem number : 17.4 (c)
Date solved : Monday, March 31, 2025 at 01:32:48 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=14 \end{align*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)-8*diff(y(x),x)+16*y(x) = 0; 
ic:=y(0) = 3, D(y)(0) = 14; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 16

ode=D[y[x],{x,2}]-8*D[y[x],x]+16*y[x]==0; 
ic={y[0]==3,Derivative[1][y][0] ==14}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.168 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) - 8*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): 14} 
dsolve(ode,func=y(x),ics=ics)
 

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