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**I have encountered a problem which needed to solve the below differential equation. The question is to solve the motion of a point mass on the xy=z surface using the Lagrangian. The exact question is as follow: A partical of mass m is constrainted to move under gravity with no friction on the surface xy=z. What is the trajectory of the particle if it starts from rest at (x,y,z) = (1, -1, -1) with the z-axis vertical.**

**And I have solved the following equation of motions:**

[tex]z\ddot{z}=mg+m\lambda[/tex]

[tex]x\ddot{x}=y\ddot{y}=C[/tex], where c is a constant

[tex]z\ddot{z}=mg+m\lambda[/tex]

[tex]x\ddot{x}=y\ddot{y}=C[/tex], where c is a constant

**Thanks!!**