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The following is an excerpt from Landau's Course on Theoretical Physics Vol.1 Mechanics:

... we should recall the fact that every first-order partial differential equation has a solution depending on an arbitrary function; such a solution is called the general integral of the equation. In mechanical applications, the general integral of the Hamilton-Jacobi equation is less important than a complete integral, which contains as many independent arbitrary constants as there are independent variables.

Can someone clarify what's a complete integral and what's a general integral of a first order partial differential equation?

Thanks.

The following is an excerpt from Landau's Course on Theoretical Physics Vol.1 Mechanics:

... we should recall the fact that every first-order partial differential equation has a solution depending on an arbitrary function; such a solution is called the general integral of the equation. In mechanical applications, the general integral of the Hamilton-Jacobi equation is less important than a complete integral, which contains as many independent arbitrary constants as there are independent variables.

Can someone clarify what's a complete integral and what's a general integral of a first order partial differential equation?

Thanks.

The following is an excerpt from Landau's Course on Theoretical Physics Vol.1 Mechanics:

... we should recall the fact that every first-order partial differential equation has a solution depending on an arbitrary function; such a solution is called the general integral of the equation. In mechanical applications, the general integral of the Hamilton-Jacobi equation is less important than a complete integral, which contains as many independent arbitrary constants as there are independent variables.

Can someone clarify what's a complete integral and what's a general integral of a first order partial differential equation?

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Complete vs General Integral of first order PDE

The following is an excerpt from Landau's Course on Theoretical Physics Vol.1 Mechanics:

... we should recall the fact that every first-order partial differential equation has a solution depending on an arbitrary function; such a solution is called the general integral of the equation. In mechanical applications, the general integral of the Hamilton-Jacobi equation is less important than a complete integral, which contains as many independent arbitrary constants as there are independent variables.

Can someone clarify what's a complete integral and what's a general integral of a first order partial differential equation?

Thanks.