lecture_19 (dragged) 3

lecture_19 (dragged) 3 - f ( t ) is the zero function, we...

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4 MA 36600 LECTURE NOTES: MONDAY, MARCH 2 This method is called Variation of Parameters . We remark that we can always write y ( t )= u 1 ( t ) y 1 ( t )+ u 2 ( t ) y 2 ( t )= c 1 y 1 ( t )+ c 2 y 2 ( t )+ Y ( t ) in terms of the function Y ( t )= ° t f ( τ ) a ( τ ) y 1 ( τ ) y 2 ( t ) y 1 ( t ) y 2 ( τ ) y 1 ( τ ) y ° 2 ( τ ) y ° 1 ( τ ) y 2 ( τ ) dτ. This function is a particular solution to the nonhomogeneous equation Note that when
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Unformatted text preview: f ( t ) is the zero function, we Fnd that u 1 ( t ) = c 1 , u 2 ( t ) = c 2 , Y ( t ) = 0 = y ( t ) = c 1 y 1 ( t ) + c 2 y 2 ( t ) . This is the general solution to the homogeneous equation....
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