58.10.36 problem 36

Internal problem ID [14723]
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 : 36
Date solved : Thursday, October 02, 2025 at 09:50:31 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=6 \\ \end{align*}

✓ Maple. Time used: 0.065 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+5*y(x) = 0; 
ic:=[y(0) = 2, D(y)(0) = 6]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 23

ode=D[y[x],{x,2}]+2*D[y[x],x]+5*y[x]==0; 
ic={y[0]==2,Derivative[1][y][0] ==6}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.099 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): 6} 
dsolve(ode,func=y(x),ics=ics)
 

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