85.33.37 problem 37

Internal problem ID [22660]
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 65
Problem number : 37
Date solved : Thursday, October 02, 2025 at 09:03:06 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.092 (sec). Leaf size: 8336

ode:=tan(x)*sin(y(x))+3*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✓ Mathematica. Time used: 0.221 (sec). Leaf size: 60

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

\begin{align*} y(x)&\to -\arccos \left (\tanh \left (\frac {1}{6} (-2 \log (\cos (x))-c_1)\right )\right )\\ y(x)&\to \arccos \left (\tanh \left (\frac {1}{6} (-2 \log (\cos (x))-c_1)\right )\right )\\ y(x)&\to 0\\ y(x)&\to -\pi \\ y(x)&\to \pi \end{align*}

✗ Sympy

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

Timed Out