46.5.4 problem 34

Internal problem ID [9613]
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 : 34
Date solved : Tuesday, September 30, 2025 at 06:21:29 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=2 \cos \left (5 t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.112 (sec). Leaf size: 21

ode:=diff(y(t),t)-y(t) = 2*cos(5*t); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = \frac {{\mathrm e}^{t}}{13}-\frac {\cos \left (5 t \right )}{13}+\frac {5 \sin \left (5 t \right )}{13} \]

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 29

ode=D[y[t],t]-y[t]==2*Cos[5*t]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^t \int _0^t2 e^{-K[1]} \cos (5 K[1])dK[1] \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t) - 2*cos(5*t) + Derivative(y(t), t),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {e^{t}}{13} + \frac {5 \sin {\left (5 t \right )}}{13} - \frac {\cos {\left (5 t \right )}}{13} \]