81.10.19 problem 14-19

Internal problem ID [21614]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 14. Second order homogeneous differential equations with constant coefficients. Page 297.
Problem number : 14-19
Date solved : Thursday, October 02, 2025 at 07:59:03 PM
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: 0.020 (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} (2 \sin (4 x)-3 \cos (4 x)) \end{align*}

✓ Sympy. Time used: 0.113 (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)
 

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