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 : Monday, January 27, 2025 at 04:59:59 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

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

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

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