85.9.9 problem 1 (i)

Internal problem ID [22483]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 37
Problem number : 1 (i)
Date solved : Thursday, October 02, 2025 at 08:40:53 PM
CAS classification : [_separable]

\begin{align*} 2 y \cos \left (x \right )+3 \sin \left (x \right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 10

ode:=2*y(x)*cos(x)+3*sin(x)*diff(y(x),x) = 0; 
ic:=[y(1/2*Pi) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {2}{\sin \left (x \right )^{{2}/{3}}} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 13

ode=2*y[x]*Cos[x]+3*Sin[x]*D[y[x],{x,1}]==0; 
ic={y[Pi/2]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2}{\sin ^{\frac {2}{3}}(x)} \end{align*}

✓ Sympy. Time used: 0.155 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x)*cos(x) + 3*sin(x)*Derivative(y(x), x),0) 
ics = {y(pi/2): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {2}{\sin ^{\frac {2}{3}}{\left (x \right )}} \]