linear_steps - GE 207K Solving First-Order Linear ODEs...

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Unformatted text preview: GE 207K Solving First-Order Linear ODEs September 1, 2010 This page aims to recap our mini-lecture on first order linear ordinary differential equations. Once a differential equation has been identified as linear and first order , i.e. the differential equation can be written in the the form y + p ( t ) y = q ( t ) , the following steps can be taken to find the general solution to the differential equation: Steps: 1. Write the given differential equation in the STANDARD FORM y + p ( t ) y = q ( t ) . (1) 2. Find the integrating factor , : ( t ) = e R p ( t ) dt . (2) 3. Multiply the BOTH sides of the Eq. (2) by the integrating factor: e R p ( t ) dt [ y + p ( t ) y ] = q ( t ) e R p ( t ) dt . (3) 4. Note that the l eft-h and-s ide (LHS) of Eq. (3) can now be re-written as d dt y e R p ( t ) dt = q ( t ) e R p ( t ) dt . (4) 5. Integrate both sides of Eq. (4). Dont forget to include the integration constant!...
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linear_steps - GE 207K Solving First-Order Linear ODEs...

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