8.4.13 problem 13

Internal problem ID [716]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 13
Date solved : Tuesday, March 04, 2025 at 11:33:55 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.130 (sec). Leaf size: 14

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)
 

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