Unformatted text preview: y ( t ) = c 1 e − t + c 2 e 4 t + ² − 2 5 t e − t ³ = ´ c 1 − 2 5 t µ e − t + c 2 e 4 t . General Method. We explain how to Fnd the general solution of the nonhomogeneous equation a ( t ) y °° + b ( t ) y ° + c ( t ) y = f ( t ) . Perform the following steps: #1. ²ind a fundamental set of solutions { y 1 , y 2 } to the homogeneous di±erential equation a ( t ) y °° + b ( t ) y ° + c ( t ) y = 0 . #2. Compute the integrals u ( t ) = − ¶ t f ( τ ) a ( τ ) y 2 ( τ ) W ( τ ) dτ + c 1 and u 2 ( t ) = ¶ t f ( τ ) a ( τ ) y 1 ( τ ) W ( τ ) dτ + c 2 in terms of the Wronskian W ( t ) = y 1 ( t ) y ° 2 ( t ) − y ° 1 ( t ) y 2 ( t ) . #3. ²orm the function y ( t ) = u 1 ( t ) y 1 ( t ) + u 2 ( t ) y 2 ( t ) . This is the general solution to the nonhomogeneous equation....
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 Spring '09
 EdrayGoins
 Derivative, general solution, dτ

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