84.37.2 problem 26.2

Internal problem ID [22344]
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 : 26.2
Date solved : Thursday, October 02, 2025 at 08:37:48 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-5 y&={\mathrm e}^{5 x} \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.032 (sec). Leaf size: 10

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

\[ y = {\mathrm e}^{5 x} x \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to \frac {1}{4} e^x \left (e^{4 x}-1\right ) \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \left (\frac {e^{4 x}}{4} - \frac {1}{4}\right ) e^{x} \]