3.7 Variation of Parameters

3.7 Variation of Parameters - M427K Variation of Parameters...

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Unformatted text preview: M427K Variation of Parameters October 10, 2011 Summary Our goal is to solve 2nd-order linear nonhomogeneous ordinary differential equations of the form y 00 + p ( t ) y + q ( t ) y = f ( t ) , (1) where p ( t ) , q ( t ) and f ( t ) are nice given functions. Recall that when using the method of undetermined coefficients, we were restricted to the type of nonhomogeneous equations we could solve. Unlike the Method of Undetermined Coefficients where we were restricted to differential equations with constant coefficients, and f ( t ) had a special form, we can use Variation of Parameters to solve any nonhomogeneous differential equation. Steps : 1. Put the differential equation in the STANDARD FORM y 00 + p ( t ) y + q ( t ) y = f ( t ) , (2) This step is essential if youre going to use the formula under Step 3ii. 2. Find the corresponding homogenous solution, y h : Set the f ( t ) equal to zero, and find the corresponding solution to the differential equa- tion. If the differential equation has constant coefficients, we would solve y 00 + ay + by = 0 (3) by writing down the characteristic equation.by writing down the characteristic equation....
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3.7 Variation of Parameters - M427K Variation of Parameters...

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