Thermodynamics HW Solutions 142

Thermodynamics HW - Chapter 2 Heat Conduction Equation 2-116C A linear homogeneous differential equation of order n is expressed in the most

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Chapter 2 Heat Conduction Equation 2-116C A linear homogeneous differential equation of order n is expressed in the most general form as y f xy f xy nn () ( ) ++ + += 1 1 1 0 L Each term in a linear homogeneous equation contains the dependent variable or one of its derivatives after the equation is cleared of any common factors. The equation is linear and homogeneous since each term is linear in y, and contains the dependent variable or one of its derivatives. ′′ −= yx y 4 2 0 0 2-117C A differential equation is said to have constant coefficients if the coefficients of all the terms which involve the dependent variable or its derivatives are constants. If, after cleared of any common factors, any of the terms with the dependent variable or its derivatives involve the independent variable as a coefficient, that equation is said to have variable coefficients The equation has variable coefficients whereas the equation y 4 2 ′′ − = yy 40 has constant coefficients.
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This note was uploaded on 01/14/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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