7.4.17 problem 17

Internal problem ID [89]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 17
Date solved : Saturday, March 29, 2025 at 04:30:52 PM
CAS classification : [_linear]

\begin{align*} \left (1+x \right ) y^{\prime }+y&=\cos \left (x \right ) \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.020 (sec). Leaf size: 14

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

\[ y = \frac {\sin \left (x \right )+1}{1+x} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 15

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

\[ y(x)\to \frac {\sin (x)+1}{x+1} \]

✓ Sympy. Time used: 0.287 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {\sin {\left (x \right )} + 1}{x + 1} \]