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 : Tuesday, March 04, 2025 at 11:48:42 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*}

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

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

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

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

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

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

✓ Sympy. Time used: 0.120 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) - exp(x) + Derivative(y(x), x),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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