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alpha25
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How can I demostrate that a solution of d2u/(dθ)^2+u=0 is u=cos(θ-θ0)
Thanks
Thanks
alpha25 said:How can I demostrate that a solution of d2u/(dθ)^2+u=0 is u=cos(θ-θ0)
Thanks
A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is often used to model physical phenomena and can be solved to find the function that satisfies the equation.
The method for solving a differential equation depends on its type and order. In general, the goal is to find a solution that satisfies the equation and any given initial conditions. This can be done analytically, using techniques such as separation of variables, or numerically, using computational methods.
The order of a differential equation is the highest derivative present in the equation. In this case, the highest derivative is d2u/(dθ)^2, so the order is 2.
The particular solution for this differential equation is u=cos(θ-θ0). This solution has been obtained by solving the equation d2u/(dθ)^2+u=0, which represents a simple harmonic motion.
θ0 represents the initial phase of the solution. It determines the starting point or position of the function u=cos(θ-θ0) on the θ-axis. Changing the value of θ0 will result in a different starting position, but the overall shape and behavior of the function will remain the same.