Internal problem ID [4006]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-y-{\mathrm e}^{x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 10
dsolve([diff(y(x),x)-y(x)=exp(x),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x} \left (x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 12
DSolve[{y'[x]-y[x]==Exp[x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (x+1) \\ \end{align*}