58.10.25 problem 25

Internal problem ID [14712]
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 : 25
Date solved : Thursday, October 02, 2025 at 09:50:24 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ y^{\prime }\left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)-diff(y(x),x)-12*y(x) = 0; 
ic:=[y(0) = 3, D(y)(0) = 5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 2 \,{\mathrm e}^{4 x}+{\mathrm e}^{-3 x} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 18

ode=D[y[x],{x,2}]-D[y[x],x]-12*y[x]==0; 
ic={y[0]==3,Derivative[1][y][0] ==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x}+2 e^{4 x} \end{align*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*y(x) - Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 e^{4 x} + e^{- 3 x} \]