76.12.6 problem 6

Internal problem ID [17562]
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 : 6
Date solved : Tuesday, January 28, 2025 at 10:44:02 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -2\right ) y^{\prime \prime }+y^{\prime }+\left (x -2\right ) \tan \left (x \right ) y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (3\right )&=1\\ y^{\prime }\left (3\right )&=2 \end{align*}

✗ Solution by Maple

dsolve([(x-2)*diff(y(x),x$2)+diff(y(x),x)+(x-2)*tan(x)*y(x)=0,y(3) = 1, D(y)(3) = 2],y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{(x-2)*D[y[x],{x,2}]+D[y[x],x]+(x-2)*Tan[x]*y[x]==0,{y[3]==1,Derivative[1][y][3]==2}},y[x],x,IncludeSingularSolutions -> True]
 

Not solved