1.10.23 problem 23

Internal problem ID [293]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 23
Date solved : Tuesday, September 30, 2025 at 03:54:38 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 )&=3 \\ y^{\prime }\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.073 (sec). Leaf size: 22

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+25*y(x) = 0; 
ic:=[y(0) = 3, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 24

ode=D[y[x],{x,2}]-6*D[y[x],x]+25*y[x]==0; 
ic={y[0]==3,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{3 x} (3 \cos (4 x)-2 \sin (4 x)) \end{align*}

✓ Sympy. Time used: 0.112 (sec). Leaf size: 20

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): 3, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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