7.3.23 problem 23

Internal problem ID [63]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 23
Date solved : Friday, February 07, 2025 at 07:47:30 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+1&=2 y \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 14

dsolve([diff(y(x),x)+1= 2*y(x),y(1) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 18

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

\[ y(x)\to \frac {1}{2} \left (e^{2 x-2}+1\right ) \]