60.1.448 problem 460

Internal problem ID [10462]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 460
Date solved : Sunday, March 30, 2025 at 04:50:10 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2}&=0 \end{align*}

✗ Maple

ode:=(diff(y(x),x)^2+y(x)^2)*cos(x)^4-a^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=-a^2 + Cos[x]^4*(y[x]^2 + D[y[x],x]^2)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

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