76.12.14 problem 25

Internal problem ID [17570]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 25
Date solved : Tuesday, January 28, 2025 at 08:28:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (1-x \cot \left (x \right )\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.249 (sec). Leaf size: 15

dsolve((1-x*cot(x))*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {csgn}\left (\sec \left (x \right )\right ) \sin \left (x \right )+c_{2} x \]

✓ Solution by Mathematica

Time used: 0.122 (sec). Leaf size: 15

DSolve[(1-x*Cot[x])*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 x+c_2 \sin (x) \]