Internal problem ID [49]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\tan \relax (x ) y^{\prime }-y=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = \frac {\pi }{2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve([tan(x)*diff(y(x),x) = y(x),y(1/2*Pi) = 1/2*Pi],y(x), singsol=all)
\[ y \relax (x ) = \frac {\pi \sin \relax (x )}{2} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 12
DSolve[{Tan[x]*y'[x] == y[x],y[Pi/2]==Pi/2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \pi \sin (x) \\ \end{align*}