26.4.3 problem 2(c)

Internal problem ID [4271]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 11, page 49
Problem number : 2(c)
Date solved : Monday, January 27, 2025 at 08:47:14 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve((1+x^2)*diff(y(x),x)+2*x*y(x)=cot(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\ln \left (\sin \left (x \right )\right )+c_{1}}{x^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 19

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

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