8.3.23 problem 24

Internal problem ID [699]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 24
Date solved : Monday, January 27, 2025 at 02:58:22 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=\frac {\pi }{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 9

dsolve([tan(x)*diff(y(x),x) = y(x),y(1/2*Pi) = 1/2*Pi],y(x), singsol=all)
 

\[ y = \frac {\pi \sin \left (x \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 12

DSolve[{Tan[x]*D[y[x],x] == y[x],y[Pi/2]==Pi/2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \pi \sin (x) \]