70.13.35 problem 35

Internal problem ID [18904]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 35
Date solved : Thursday, October 02, 2025 at 03:32:40 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-2 \\ y^{\prime }\left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 12

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

\[ y = -1-{\mathrm e}^{-3 x} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 14

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

\begin{align*} y(x)&\to -e^{-3 x}-1 \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = -1 - e^{- 3 x} \]