32.5.20 problem Exercise 11.21, page 97

Internal problem ID [5858]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.21, page 97
Date solved : Monday, January 27, 2025 at 01:21:02 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 10

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

\[ y \left (x \right ) = {\mathrm e}^{x} \left (x +1\right ) \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 12

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

\[ y(x)\to e^x (x+1) \]