3.13 problem 13

Internal problem ID [4265]

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: 13.
ODE order: 1.
ODE degree: 1.

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

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

Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(diff(x(y),y)+(x(y)-exp(y))=0,x(y), singsol=all)
 

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

Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 21

DSolve[x'[y]+(x[y]-Exp[y])==0,x[y],y,IncludeSingularSolutions -> True]
 

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