64.10.38 problem 38

Internal problem ID [13365]
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 : 38
Date solved : Wednesday, March 05, 2025 at 09:49:12 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+37 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-4 \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 22

ode:=4*diff(diff(y(x),x),x)+4*diff(y(x),x)+37*y(x) = 0; 
ic:=y(0) = 2, D(y)(0) = -4; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 26

ode=4*D[y[x],{x,2}]+4*D[y[x],x]+37*y[x]==0; 
ic={y[0]==2,Derivative[1][y][0] ==-4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x/2} (2 \cos (3 x)-\sin (3 x)) \]

✓ Sympy. Time used: 0.179 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(37*y(x) + 4*Derivative(y(x), x) + 4*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): -4} 
dsolve(ode,func=y(x),ics=ics)
 

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