84.37.5 problem 26.5

Internal problem ID [22347]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 26. Solutions of linear differential equations with constant coefficients by Laplace transform. Solved problems. Page 159
Problem number : 26.5
Date solved : Thursday, October 02, 2025 at 08:37:49 PM
CAS classification : [[_2nd_order, _missing_x]]

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

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.043 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)+4*y(x) = 0; 
ic:=[y(0) = 2, D(y)(0) = 2]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

\[ y = 2 \cos \left (2 x \right )+\sin \left (2 x \right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.033 (sec). Leaf size: 14

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

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