67.2.28 problem Problem 5(b)

Internal problem ID [13985]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 5(b)
Date solved : Tuesday, January 28, 2025 at 08:25:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{4}\right )&=1\\ y^{\prime }\left (\frac {\pi }{4}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 20.079 (sec). Leaf size: 1300

dsolve([diff(y(x),x$2)+tan(x)*diff(y(x),x)+cot(x)*y(x)=0,y(1/4*Pi) = 1, D(y)(1/4*Pi) = 0],y(x), singsol=all)
 

\[ \text {Expression too large to display} \]

✗ Solution by Mathematica

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

DSolve[{D[y[x],{x,2}]+Tan[x]*D[y[x],x]+Cot[x]*y[x]==0,{y[Pi/4]==1,Derivative[1][y][Pi/4]==0}},y[x],x,IncludeSingularSolutions -> True]
 

Not solved