58.10.28 problem 28

Internal problem ID [14715]
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 : 28
Date solved : Thursday, October 02, 2025 at 09:50:26 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime }+4 y^{\prime }-4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=-4 \\ \end{align*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 10

ode:=3*diff(diff(y(x),x),x)+4*diff(y(x),x)-4*y(x) = 0; 
ic:=[y(0) = 2, D(y)(0) = -4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 2 \,{\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 12

ode=3*D[y[x],{x,2}]+4*D[y[x],x]-4*y[x]==0; 
ic={y[0]==2,Derivative[1][y][0] ==-4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.102 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) + 4*Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): -4} 
dsolve(ode,func=y(x),ics=ics)
 

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