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    Differential equations

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    section 4.3 # 4,16,22,34,38

    See attached

    The auxiliary equation for the given differential equation has complex roots. Find a general solution.
    Solve the given initial value problem.
    Prove the sum of angle formula for the sine function by following these steps.

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    4. if the auxiliary equation has complex roots , the general solution has the form of , where C1 and C2 are both constants
    The auxiliary equation is

    The roots are:

    Then the general solution is

    16. The auxiliary equation is

    The roots are:

    Since the auxiliary equation has two district real roots, the general solution ...

    Solution Summary

    This provides several examples of working with differential equations, including initial value problem, complex roots, a proof of the sum of angle formula, and an RLC series circuit.