76.4.20 problem 26

Internal problem ID [17414]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 10:06:25 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&={\mathrm e}^{2 x}+y-1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve(diff(y(x),x)=exp(2*x)+y(x)-1,y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x}+1+{\mathrm e}^{x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 18

DSolve[D[y[x],x]==Exp[2*x]+y[x]-1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x}+c_1 e^x+1 \]