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coolxal
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How do you change the form of a differential equation from dy/dt to f(y,t)? So if I had dy/dx = y/A(y) + 1 where A(y) is the area of a cross section of a conical base.
A differential equation is an equation that relates a function to its derivatives. It describes the relationship between a function and its rate of change.
Differential equations are used to model many real-world phenomena, such as population growth, chemical reactions, and electrical circuits. Solving them allows us to make predictions and understand the behavior of these systems.
dy/dt is the notation for the derivative of a function y with respect to the independent variable t. It represents the instantaneous rate of change of y with respect to t.
The specific method for solving a differential equation depends on its type and order. Some common techniques include separation of variables, substitution, and using integrating factors. It is important to also use initial or boundary conditions to find the specific solution.
f(y,t) represents the function that relates the derivative dy/dt to the variables y and t. It is typically given in the form of an expression or an equation and is used to solve for the values of y and t that satisfy the differential equation.