85.2.5 problem 4

Internal problem ID [22432]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. B Exercises at page 14
Problem number : 4
Date solved : Thursday, October 02, 2025 at 08:39:17 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 15

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

\[ y = \frac {12 \,{\mathrm e}^{x}}{5}+\frac {3 \,{\mathrm e}^{-4 x}}{5} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to \frac {3}{5} e^{-4 x} \left (4 e^{5 x}+1\right ) \end{align*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \frac {12 e^{x}}{5} + \frac {3 e^{- 4 x}}{5} \]