10.7.14 problem 14

Internal problem ID [1262]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 14
Date solved : Saturday, March 29, 2025 at 10:50:31 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+y^{\prime }-4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.125 (sec). Leaf size: 20

ode:=2*diff(diff(y(x),x),x)+diff(y(x),x)-4*y(x) = 0; 
ic:=y(0) = 0, D(y)(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {4 \,{\mathrm e}^{-\frac {x}{4}} \sqrt {33}\, \sinh \left (\frac {x \sqrt {33}}{4}\right )}{33} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 40

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

\[ y(x)\to \frac {2 e^{-\frac {1}{4} \left (1+\sqrt {33}\right ) x} \left (e^{\frac {\sqrt {33} x}{2}}-1\right )}{\sqrt {33}} \]

✓ Sympy. Time used: 0.172 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) + Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {2 \sqrt {33} e^{\frac {x \left (-1 + \sqrt {33}\right )}{4}}}{33} - \frac {2 \sqrt {33} e^{- \frac {x \left (1 + \sqrt {33}\right )}{4}}}{33} \]