56.4.32 problem 28

Internal problem ID [8921]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 28
Date solved : Sunday, March 30, 2025 at 01:53:27 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} {y^{\prime }}^{2}+y^{2}&=\sec \left (x \right )^{4} \end{align*}

✗ Maple

ode:=diff(y(x),x)^2+y(x)^2 = sec(x)^4; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]^2+y[x]^2==Sec[x]^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**2 + Derivative(y(x), x)**2 - 1/cos(x)**4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(-y(x)**2*cos(x)**4 + 1)/cos(x)**2 + Derivative(y(x), x) cannot be solved by the factorable group method