Ordinary Differential Equations

Ordinary Differential Equations - 1 Tuesday, October 27,...

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Tuesday, October 27, 2009 Ordinary Differential Equations (ODEs) Linear Non Linear = = + dxdt x Atx bt = , x ft x = ° x0 x = ° x0 x Usual substitution = + x Ax bt This can be solved analytically System of Linear ODEs = + x Ax bt ; = ° x0 x Scalar Case = = + - = dxdt x ax bt dxdt ax bt Integrating factor - e at - = dxdt atx bt IF - ( ) e a t dt - - → - + - (- ) e atdxdt ax e atdxdt xde atdt a | | - ddte atx - - = - → = - = ( ) - e atbt ddte atx bte at t 0tde atx 0tb t e atdt - + - - = - - e atdxdt xe at a e atdxdt x
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Unformatted text preview: 1 Tuesday, October 27, 2009 Note: there is t and t’-=-→ --=-→ e at0t 0tbt'e at'dt' e atxt e0x0 0tbt'e at'dt' | | x-= +-→ = -+ --e atxt x0 0tbt'e at'dt xt e atx0 e at0tbt'e at'dt' 51 IF b(t)=b constant multiply by -a/-a = 1-= -= ---= --=---0tbt'e at'dt' b0te at'dt' b a0te at'd at' bae at'0t bae at e0 So for constant b = -+ ---- → = --- -xt e atx0 e at bae at 1 xt e atx0 ba1 e at52 2...
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This note was uploaded on 01/08/2010 for the course COT 3502 taught by Professor Hawkins during the Fall '08 term at University of Florida.

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Ordinary Differential Equations - 1 Tuesday, October 27,...

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