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Economics Dynamics Problems 54

# Economics Dynamics Problems 54 - 38 Economic Dynamics Step...

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38 Economic Dynamics Step 2 Calculate the integrating factor µ ( t ) = e p ( t ) dt Step 3 Multiply throughout by the integrating factor, integrate both sides and add a constant of integration to the right-hand side (a) µ ( t ) dy dt + p ( t ) y = µ ( t ) g ( t ) or d dt [ µ ( t ) y ] = µ ( t ) g ( t ) (b) d dt [ µ ( t ) y ] dt = µ ( t ) g ( t ) dt + c Step 4 Write the general result µ ( t ) y = µ ( t ) g ( t ) + c Example 2.10 As an example, let us apply this four-step procedure to the equation dy dt = a + by Step 1 We can write this in the standard form dy dt by = a Step 2 Calculate the integrating factor
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