6.2.25 problem 25

Internal problem ID [1561]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 25
Date solved : Tuesday, September 30, 2025 at 04:36:25 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+7 y&={\mathrm e}^{3 x} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.032 (sec). Leaf size: 17

ode:=diff(y(x),x)+7*y(x) = exp(3*x); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{3 x}}{10}-\frac {{\mathrm e}^{-7 x}}{10} \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 21

ode=D[y[x],x] +7*y[x]==Exp[3*x]; 
ic=y[0]==0; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{10} e^{-7 x} \left (e^{10 x}-1\right ) \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(7*y(x) - exp(3*x) + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {e^{3 x}}{10} - \frac {e^{- 7 x}}{10} \]