8.9.12 problem 23

Internal problem ID [856]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.3, second order linear equations. Page 323
Problem number : 23
Date solved : Tuesday, March 04, 2025 at 11:54:00 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+25*y(x) = 0; 
ic:=y(0) = 4, D(y)(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{3 x} \left (11 \sin \left (4 x \right )-16 \cos \left (4 x \right )\right )}{4} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 27

ode=D[y[x],{x,2}]-6*D[y[x],x]+25*y[x]==0; 
ic={y[0]==4,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} e^{3 x} (16 \cos (4 x)-11 \sin (4 x)) \]

✓ Sympy. Time used: 0.178 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*y(x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 4, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (- \frac {11 \sin {\left (4 x \right )}}{4} + 4 \cos {\left (4 x \right )}\right ) e^{3 x} \]