52.5.2 problem 32

Internal problem ID [8325]
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 : Monday, January 27, 2025 at 03:49:03 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*}

✓ Solution by Maple

Time used: 0.590 (sec). Leaf size: 10

dsolve([2*diff(y(t),t)+y(t)=0,y(0) = -3],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 14

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

\[ y(t)\to -3 e^{-t/2} \]