84.37.3 problem 26.3

Internal problem ID [22345]
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. Solved problems. Page 159
Problem number : 26.3
Date solved : Thursday, October 02, 2025 at 08:37:49 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-5 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (\pi \right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 14

ode:=diff(y(x),x)-5*y(x) = 0; 
ic:=[y(Pi) = 2]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to 2 e^{5 x-5 \pi } \end{align*}

✓ Sympy. Time used: 0.062 (sec). Leaf size: 14

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

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