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Complete the passage with the words and phrases from the following list:

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arbitrary
direction field
displaced vertically
general
highest order
integration
p
articular
with respect to
 

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A [[0]] solution of a differential equation is a solution that contains [[1]] constants. These constants can be chosen to satisfy specific conditions, resulting in a [[2]] solution.

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The process of finding the general solution of a differential equation is called anti-differentiation, or [[3]].

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The symbol $\\frac{dy}{dx}$ means the derivative of $y$ [[4]] $x$, and can be read simply as \"d y d x\".

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The differential equation $y''+y=0$ is a second-order differential equation because the [[5]] derivative is $y''$.

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A [[6]] is a graphical representation of the solutions of a differential equation. It can be used to visualize the behavior of the solutions and to make predictions about their values.

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The solution curve of a differential equation can be [[7]] by adding a constant to it.

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