87.12.14 problem 15

Internal problem ID [23462]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 93
Problem number : 15
Date solved : Thursday, October 02, 2025 at 09:42:01 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ y^{\prime }\left (0\right )&=-6 \sqrt {3} \\ \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)+3*y(x) = 0; 
ic:=[y(0) = 3, D(y)(0) = -6*3^(1/2)]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -6 \sin \left (\sqrt {3}\, x \right )+3 \cos \left (\sqrt {3}\, x \right ) \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 26

ode=D[y[x],{x,2}]+3*y[x]==0; 
ic={y[0]==3,Derivative[1][y][0] ==-6*Sqrt[3]}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 \left (\cos \left (\sqrt {3} x\right )-2 \sin \left (\sqrt {3} x\right )\right ) \end{align*}

✓ Sympy. Time used: 0.048 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): -6*sqrt(3)} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 6 \sin {\left (\sqrt {3} x \right )} + 3 \cos {\left (\sqrt {3} x \right )} \]