5_pdfsam_math 54 differential equation solutions odd

5_pdfsam_math 54 differential equation solutions odd -...

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CHAPTER 1: Introduction EXERCISES 1.1: Background, page 5 1. This equation involves only ordinary derivatives of x with respect to t , and the highest deriva- tive has the second order. Thus it is an ordinary diFerential equation of the second order with independent variable t and dependent variable x . It is linear because x , dx/dt ,and d 2 x/dt 2 appear in additive combination (even with constant coefficients) of their ±rst powers. 3. This equation is an ODE because it contains no partial derivatives. Since the highest order derivative is dy/dx , the equation is a ±rst order equation. This same term also shows us that the independent variable is x and the dependent variable is y . This equation is nonlinear because of the y in the denominator of the term [ y (2 3 x )] / [ x (1 3 y )] . 5. This equation is an ODE because it contains only ordinary derivatives. The term dp/dt is the highest order derivative and thus shows us that this is a ±rst order equation. This term also
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Unformatted text preview: shows us that the independent variable is t and the dependent variable is p . This equation is nonlinear since in the term kp ( P − p ) = kP p − kp 2 the dependent variable p is squared (compare with equation (7) on page 5 of the text). 7. This equation is an ordinary ±rst order diFerential equation with independent variable x and dependent variable y . It is nonlinear because it contains the square of dy/dx . 9. This equation contains only ordinary derivative of y with respect to x . Hence, it is an ordi-nary diFerential equation of the second order (the highest order derivative is d 2 y/dx 2 ) with independent variable x and dependent variable y . This equation is of the form (7) on page 5 of the text and, therefore, is linear. 1...
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at Berkeley.

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