4.7.10 problem 10

Internal problem ID [1258]
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 : 10
Date solved : Tuesday, September 30, 2025 at 04:31:47 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.053 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)+3*y(x) = 0; 
ic:=[y(0) = 2, D(y)(0) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {5 \,{\mathrm e}^{-x}}{2}-\frac {{\mathrm e}^{-3 x}}{2} \]

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

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

\begin{align*} y(x)&\to \frac {1}{2} e^{-3 x} \left (5 e^{2 x}-1\right ) \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (\frac {5}{2} - \frac {e^{- 2 x}}{2}\right ) e^{- x} \]