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d2P/dV2 = 2RT(V - b)-3 + a[(2*sqrt(T))*(V2sqrt(T) + Vb*sqrt(T))-2 - 2(V2*sqrt(T) + V*sqrt(T))-3*(2V*sqrt(T) + b*sqrt(T))2]

Q: What are the first and second partial derivates of the redlich-kwong equation of state with respect to V and with constant T?

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It is just one component of the fully completed equation.

ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.

Yes, it is.

partial of u with respect to x = partial of v with respect to y partial of u with respect to y = -1*partial of v with respect to x

Some partial differential equations do not have analytical solutions. These can only be solved numerically.

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It is just one component of the fully completed equation.

ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.

Yes, it is.

partial of u with respect to x = partial of v with respect to y partial of u with respect to y = -1*partial of v with respect to x

The lagrange function, commonly denoted L is the lagrangian of a system. Usually it is the kinetic energy - potential energy (in the case of a particle in a conservative potential). The lagrange equation is the equation that converts a given lagrangian into a system of equations of motion. It is d/dt(\partial L/\partial qdot)-\partial L/\partial q.

PDE stands for Partial Differential Equation

Some partial differential equations do not have analytical solutions. These can only be solved numerically.

partial vx w/ respect to x + partial vy w/ respect to y + partial vz w/ respect to z = 0

The partial derivative only acts on one the variables on the equations and treats the others as constant.

Poisson's equation is a partial differential equation of elliptic type. it is used in electrostatics, mechanical engineering and theoretical physics.

An ordinary differential equation (ODE) has only derivatives of one variable.