35.3.13 problem 13

Internal problem ID [6117]
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
Date solved : Monday, January 27, 2025 at 01:36:27 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} x^{\prime }+x-{\mathrm e}^{y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (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: 0.042 (sec). Leaf size: 21

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

\[ x(y)\to \frac {e^y}{2}+c_1 e^{-y} \]