12.2.21 problem 21

Internal problem ID [1557]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 21
Date solved : Saturday, March 29, 2025 at 10:58:58 PM
CAS classification : [_linear]

\begin{align*} \left (1+x \right ) y^{\prime }+2 y&=\frac {\sin \left (x \right )}{1+x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=(1+x)*diff(y(x),x)+2*y(x) = sin(x)/(1+x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\cos \left (x \right )+c_1}{\left (1+x \right )^{2}} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 18

ode=(1+x)*D[y[x],x] +2*y[x]==Sin[x]/(1+x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {-\cos (x)+c_1}{(x+1)^2} \]

✓ Sympy. Time used: 0.436 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 1)*Derivative(y(x), x) + 2*y(x) - sin(x)/(x + 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} - \cos {\left (x \right )}}{x^{2} + 2 x + 1} \]