85.9.7 problem 1 (g)

Internal problem ID [22481]
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 (g)
Date solved : Thursday, October 02, 2025 at 08:40:47 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{4}\right )&=\frac {\pi }{4} \\ \end{align*}

✓ Maple. Time used: 0.152 (sec). Leaf size: 11

ode:=sin(y(x))^2+cos(x)^2*diff(y(x),x) = 0; 
ic:=[y(1/4*Pi) = 1/4*Pi]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\pi }{2}-x \]

✓ Mathematica. Time used: 0.189 (sec). Leaf size: 8

ode=Sin[y[x]]^2+Cos[x]^2*D[y[x],{x,1}]==0; 
ic={y[Pi/4]==Pi/4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \cot ^{-1}(\tan (x)) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sin(y(x))**2 + cos(x)**(2**Derivative(y(x), x)),0) 
ics = {y(pi/4): pi/4} 
dsolve(ode,func=y(x),ics=ics)
 

IndexError : Index out of range: a[1]