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The general solution of the differential equation.
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Answer to Problem 1P
The general solution of the initial value problem is
Explanation of Solution
Formula used:
The variation of parameters for higher order differential equations is
Calculation:
Consider the differential equation
The characteristic polynomial for the equation is
Obtain the root of the equation as follows.
The roots are
Therefore, the complimentary solution of the equation is
A fundamental set of solutions
Then the general solution of the homogeneous equation is
Solving the fundamental set
Compute the latter determinant by minors as follows.
Similarly,
By using the variation of parameters formula for obtain the particular solution.
Similarly,
Therefore, the particular solution is
Hence, the general solution of the initial value problem is
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Chapter 4 Solutions
Elementary Differential Equations
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