7.3.24 problem 24

Internal problem ID [64]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 24
Date solved : Friday, February 07, 2025 at 07:47:32 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: 0.005 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 12

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

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