FirstOrderLinear - First Order Linear Equations The general...

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Unformatted text preview: First Order Linear Equations The general first order linear equation is of the form dy dt + p ( t ) y = g ( t ) , (1) where p and g are given functions of t . The general method for solving such equations is to find an integrating factor , i.e., a function μ ( t ) such that if we multiply (1) by μ ( t ), we can rewrite the resulting equation μ ( t ) dy dt + p ( t ) μ ( t ) y = μ ( t ) g ( t ) as d dt ( μ ( t ) y ) = μ ( t ) g ( t ) , (2) which can be easily solved by the taking the integral of both sides. We have seen that the integrating factor is given by the formula μ ( t ) = e R p ( t ) dt . (3) Warning: This formula only works for equations of the form (1), so it is necessary that the coefficient in front of the dy dt term is 1. If that is not the case you first have to divide by a function of t to make it so. Example 1 Find the general solution of the differential equation dy dt + ty = t....
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This note was uploaded on 05/24/2011 for the course MAT 244 taught by Professor Christinasaleh during the Spring '10 term at University of Toronto.

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FirstOrderLinear - First Order Linear Equations The general...

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