Differential Equations Flashcard

Front

Define a differential equation.

Back

A differential equation is an equation that relates a function with its derivatives. It describes how a quantity changes in relation to another quantity.

Front

What is the general solution of a first-order linear differential equation?

Back

Front

Solve the differential equation: dy/dx = (y+5)(x+2).

Back

Front

What is the method of separation of variables?

Back

The method of separation of variables involves rearranging a differential equation to isolate the variables on opposite sides, allowing for integration of both sides.

Front

Solve the differential equation: dy/dx = x(y+5).

Back

Front

What is an initial condition in the context of differential equations?

Back

An initial condition specifies the value of the function at a particular point, allowing for the determination of the constant in the general solution.

Front

Solve the differential equation: dy/dx = (y+5)(x+2) given the point (0,1).

Back

Front

What is the solution to the differential equation dy/dx = x^2/y with the initial condition y(3) = -2?

Back

Front

Solve the differential equation: dy/dx = xy + 2y.

Back

Front

What is a homogeneous differential equation?

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