1. classification and integrating factors.pdf

1. classification and integrating factors.pdf - Worksheet 1...

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Worksheet 1 Classification and Integrating Factors The following equations are all examples of [check one] (a) Ordinary Differential Equations (ODEs). (b) Partial Differential Equations (PDEs). For questions 1-10, give the order of the equation and indicate if it is linear or nonlinear . 1. t 2 y 00 + ty 0 + 2 y = sin( t ) 2. (1 + y 2 ) y 00 + ty 0 + y = e t 3. y (4) + y 000 + y 00 + y 0 + y = 1 4. y 0 + ty 2 = 0 5. y 00 + sin( t + y ) = sin( t ) 6. y 000 + ty 0 + ( cos 2 ( t ) ) y = t 3 7. y 000 y 00 y 0 yt = sin( t ) 8. y sin( t ) - 4 y 0 cos ( sin( t ) ) = y 0 - 6 9. y (5) log( t ) + y 0 log ( log( t ) ) = sin( t ) 10. log( y 00 ) t + log( y ) cos( t ) = 3 sin( t ) (Questions 1-6 are taken from Boyce & DiPrima section 1.3) 1
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For each of the following linear, first-order ODEs , use the method of integrating factors to (i) find an integrating factor μ
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