8.3.22 problem 23

Internal problem ID [698]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 23
Date solved : Monday, January 27, 2025 at 02:58:20 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 18

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

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