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Unformatted text preview: tions. This is one type of diﬀerential equations you’re going to see in class many times. So it’s helpful for you to remember or refer to this. dx dt = ax + b, → dx ax + b = dt, → d ( x + b a ) a ( x + b a ) = dt, ( ∵ dx = d ( x + b a )) → 1 a Z d ( x + b a ) ( x + b a ) = Z dt, → 1 a ln ( x + b a ) = t + C, → ln ( x + b a ) = at + C , → e at + C = x + b a , → x ( t ) = e at + Cb a , → x ( t ) = e C e atb a , depending on given initial condition , → x ( t ) = ( x + b a ) e atb a , ( ∵ x = x (0) = e Cb a ) or → x ( t ) = ( x t * + b a ) e a ( tt * )b a , ( ∵ x t * = x ( t * ) = e C e at *b a )...
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This note was uploaded on 06/16/2010 for the course MS&E 249 taught by Professor Olivierdelagrandville during the Fall '08 term at Stanford.
 Fall '08
 OLIVIERDELAGRANDVILLE

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