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 : Tuesday, March 04, 2025 at 11:33:03 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*}

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

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

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 12

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

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

✓ Sympy. Time used: 0.226 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + tan(x)*Derivative(y(x), x),0) 
ics = {y(pi/2): pi/2} 
dsolve(ode,func=y(x),ics=ics)
 

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