Internal problem ID [4264]
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`]]
\[ \boxed {x^{\prime }+x-{\mathrm e}^{y}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(x(y),y)+(x(y)-exp(y))=0,x(y), singsol=all)
\[ x \left (y \right ) = \frac {{\mathrm e}^{y}}{2}+{\mathrm e}^{-y} c_{1} \]
✓ Solution by Mathematica
Time used: 0.04 (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*}