46.5.2 problem 32

Internal problem ID [9611]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. 7.2.2 TRANSFORMS OF DERIVATIVES Page 289
Problem number : 32
Date solved : Tuesday, September 30, 2025 at 06:21:28 PM
CAS classification : [_quadrature]

\begin{align*} 2 y^{\prime }+y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.083 (sec). Leaf size: 10

ode:=2*diff(y(t),t)+y(t) = 0; 
ic:=[y(0) = -3]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 14

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

\begin{align*} y(t)&\to -3 e^{-t/2} \end{align*}

✓ Sympy. Time used: 0.068 (sec). Leaf size: 10

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

\[ y{\left (t \right )} = - 3 e^{- \frac {t}{2}} \]