3.1 problem 1

Internal problem ID [4253]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number: 1.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_linear, class A]]

Solve \begin {gather*} \boxed {y^{\prime }+y-{\mathrm e}^{x}=0} \end {gather*}

Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve(diff(y(x),x)+y(x)=exp(x),y(x), singsol=all)
 

\[ y \relax (x ) = \frac {{\mathrm e}^{x}}{2}+{\mathrm e}^{-x} c_{1} \]

Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 21

DSolve[y'[x]+y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {e^x}{2}+c_1 e^{-x} \\ \end{align*}