84.38.3 problem 26.15

Internal problem ID [22357]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 26. Solutions of linear differential equations with constant coefficients by Laplace transform. Supplementary problems
Problem number : 26.15
Date solved : Thursday, October 02, 2025 at 08:37:54 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+2 y&={\mathrm e}^{t} \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.034 (sec). Leaf size: 15

ode:=diff(y(t),t)+2*y(t) = exp(t); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.077 (sec). Leaf size: 15

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

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