# How do you find a Power Series solution of a nonhomogeneous differential equation?

This may add considerable effort to the solution and if the power series solution can be identified as an elementary function, it's generally easier to just solve the homogeneous equation and use either the method of undetermined coefficients or the method of variation of parameters.

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To find a power series solution of a nonhomogeneous differential equation, follow these steps:

- Solve the homogeneous part of the equation to find the complementary solution.
- Assume the particular solution has a power series representation and substitute it into the nonhomogeneous equation.
- Equate coefficients of like powers of the variable in the equation.
- Solve for the coefficients of the power series by solving the resulting recurrence relations.
- Combine the complementary solution with the particular solution to get the general solution of the nonhomogeneous equation.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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