while solving Lagrangian of a system to derive equations of motion in presence of a constraint, I have finally landed down to a system of 3 coupled ODEs , where i have two variables(x and y) and 1 Lagrange multiplier.(adsbygoogle = window.adsbygoogle || []).push({});

ODEs are of order 4,3 and 1 respectively.

L_{1}(x,y)=lambda

L_{2}(x,y)=0

C(x,y)=0

where L1 and L2 are odes and C is the constraint

Now how to solve such a system. Any suggestions?

My attempt was:

after deriving ODEs L1 and L2, i applied constraint and got these 2 ODEs in one variable by replacing another one, but i am still confused, these two ODEs will give the same solution? or i need to manipulate between these two as well?

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# System of ODE

Can you offer guidance or do you also need help?

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