20.3.19 problem Problem 19

Internal problem ID [3628]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 19
Date solved : Monday, January 27, 2025 at 07:47:53 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve([y(x)-exp(x)+diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[{y[x]-Exp[x]+D[y[x],x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

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