second_order

second_order - / ( 2 a ) + c 2 xe-bx / ( 2 a ) If b 2-4 ac...

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General Solution to a Linear Second Order Differential Equation with Constant Coefficients a d 2 y dx 2 + b dy dx + cy = 0 , ( a 6 = 0 ) (1) General solution: If b 2 - 4 ac > 0, let r 1 = - b - b 2 - 4 ac 2 a , r 2 = - b + b 2 - 4 ac 2 a . The general solution is y ( x ) = c 1 e r 1 x + c 2 e r 2 x If b 2 - 4 ac = 0, the general solution is y ( x ) = c 1 e - bx
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Unformatted text preview: / ( 2 a ) + c 2 xe-bx / ( 2 a ) If b 2-4 ac < 0, let = 4 ac-b 2 2 a . The general solution is y ( x ) = c 1 e-bx / ( 2 a ) cos ( x )+ c 2 e-bx / ( 2 a ) sin ( x ) 1...
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