12.2.25 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 : Monday, January 27, 2025 at 05:00:10 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*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 16

dsolve([diff(y(x),x) +7*y(x)=exp(3*x),y(0) = 0],y(x), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{10 x}-1\right ) {\mathrm e}^{-7 x}}{10} \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{10} e^{-7 x} \left (e^{10 x}-1\right ) \]