Euler Lagrange Equation to Solve a Functional

We use the Euler Lagrange Equation to solve a functional given y(0)=0.
F(y',y,x) = y^2 y'^2 .
We use auxiliary equations to solve the Euler Lagrange equation r^2+1=0 .
Which gives us equal complex solutions so we use y = A cos(X) + B Sin(X)

#functionalanalysis
#functional
#calculus
#calculusofvariations
#calculusofvariation
#multivariablecalculus
#multivariable
#partial_differentiation
#partialderivatives
#partialdifferentiation