87.12.15 problem 16

Internal problem ID [23463]
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 : 16
Date solved : Thursday, October 02, 2025 at 09:42:03 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 10

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

\[ y = 2 \sinh \left (2 x \right ) \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to e^{-2 x} \left (e^{4 x}-1\right ) \end{align*}

✓ Sympy. Time used: 0.055 (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): 0, Subs(Derivative(y(x), x), x, 0): 4} 
dsolve(ode,func=y(x),ics=ics)
 

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