85.32.1 problem 1

Internal problem ID [22623]
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. C Exercises at page 64
Problem number : 1
Date solved : Sunday, October 12, 2025 at 05:53:28 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y&=y^{\prime } \tan \left (x \right )-{y^{\prime }}^{2} \sec \left (x \right )^{2} \end{align*}

✓ Maple. Time used: 0.160 (sec). Leaf size: 21

ode:=y(x) = diff(y(x),x)*tan(x)-diff(y(x),x)^2*sec(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\sin \left (x \right )^{2}}{4} \\ y &= c_{1} \left (\sin \left (x \right )-c_{1} \right ) \\ \end{align*}

✓ Mathematica. Time used: 1.752 (sec). Leaf size: 30

ode=y[x]==D[y[x],{x,1}]*Tan[x]- D[y[x],{x,1}]^2*Sec[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{4} c_1 (-2 \sin (x)+c_1)\\ y(x)&\to \frac {\sin ^2(x)}{4} \end{align*}

✗ Sympy

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

Timed Out