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Join in expert discussion on differential equation topics like ODE and PDE. Differential equations are an equation involving derivatives of a function or functions.

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Generally, Differential equations are basis for every meaningful physical theory in existence.
They are the starting point for the math. DEqs are the mathematical language to express how things change.

All of our physical observations are in the terms of how things change. If you translate the observed changes in the physical world carefully into mathematics you have a differential equation. Solve the differential equations and you have a tool to make a physical prediction.

All of our physical observations are in the terms of how things change. If you translate the observed changes in the physical world carefully into mathematics you have a differential equation. Solve the differential equations and you have a tool to make a physical prediction.