Internal problem ID [13369]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page
103
Problem number: 5.3 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+5 y={\mathrm e}^{-3 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve([diff(y(x),x)+5*y(x)=exp(-3*x),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left ({\mathrm e}^{2 x}-1\right ) {\mathrm e}^{-5 x}}{2} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 21
DSolve[{y'[x]+5*y[x]==Exp[-3*x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-5 x} \left (e^{2 x}-1\right ) \]