73.10.4 problem 15.2 (d)

Internal problem ID [15220]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.2 (d)
Date solved : Thursday, March 13, 2025 at 05:49:46 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=6 \end{align*}

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

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+4*y(x) = 0; 
ic:=y(0) = 1, D(y)(0) = 6; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \left (4 x +1\right ) \]

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

ode=D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==0; 
ic={y[0]==1,Derivative[1][y][0] ==6}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} (4 x+1) \]

✓ Sympy. Time used: 0.183 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 6} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (4 x + 1\right ) e^{2 x} \]