Find the general solution to the differential equation. (d...

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Key Concepts

Differential Equations

Differential equations are mathematical expressions that relate a function to its derivatives. They appear in various fields such as physics, engineering, and economics to describe how a quantity changes with respect to another one, like time or space. Solving a differential equation involves finding a function or a set of functions that satisfy the relationship imposed by the equation.

Antiderivatives and Indefinite Integration

Antiderivatives, or indefinite integrals, are functions whose derivative is the given function. In the context of solving a differential equation like dy/dx = cos x, one can integrate the right-hand side with respect to x to find the antiderivative. This process effectively 'reverses' differentiation, leading to the general solution of the differential equation.

Constant of Integration

When performing indefinite integration, an arbitrary constant of integration is added to the result because the derivative of a constant is zero. This constant represents the family of all solutions to the differential equation, ensuring that the general solution can account for an initial condition if one is provided.

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