64.10.33 problem 33

Internal problem ID [13368]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 33
Date solved : Monday, March 31, 2025 at 07:52:30 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+29 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+29*y(x) = 0; 
ic:=y(0) = 0, D(y)(0) = 5; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \sin \left (5 x \right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 15

ode=D[y[x],{x,2}]-4*D[y[x],x]+29*y[x]==0; 
ic={y[0]==0,Derivative[1][y][0] ==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} \sin (5 x) \]

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

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(29*y(x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = e^{2 x} \sin {\left (5 x \right )} \]