Q:

# What are some tips for solving differential equations?

A:

It is important to spend time learning the different types of differential equations and how to distinguish between them. Once a person learns how to classify differential equations, she needs only to learn and apply the different methods for efficiently solving each type of equation.

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To classify an equation, a person must learn which symbols are constants and which symbols vary. Authors write equations in different ways that often mean the same thing, so one tip for solving differential equations is to study the various ways that authors write them. For example, some textbooks use a modified format for lengthy exponential numbers, and other textbooks only use the standard format.

Like solving basic integrations, to solve a differential equation, a person first finds the general solution and then substitutes various numbers to find particular solutions. Finding the general solution involves an unknown constant, and finding the particular solution requires solving for the constant. Depending on the type of problem, it might work best to solve for constants with each level of integration, or it might work best to wait until the very end and solve for all of the constants at once. Identifying proper mathematical order helps to solve a differential equation and also helps to identify which functions contain derivatives and which functions do not contain derivatives.

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