summary-differential-eqs

summary-differential-eqs -...

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Solution of First Order Differential Equations ( 29 x f dx dy = by direct integration ( 29 ( 29 y g x f dx dy =      (separable equation) by separation of variables ( 29 ( 29 x Q y x P dx dy = +      (linear equation) rearrange equation so that it resembles the  general form (above) identify  ( 29 x P calculate the integrating factor,  Pdx e multiply through by the integrating factor remember lhs can then be expressed as  ( × y dx d  integrating factor 29 then integrate both sides wrt  x
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Solution of Second Order Linear Differential Equations with  Constant Coefficients Homogeneous Equation 0 2 2 = + + cy dx dy b dx y d a where a , b and c are constants Form the auxiliary equation 0 2 = + + c bm am If roots are real and different 1 m m = and 2 m then general solution is x m x m Be Ae y 2 1 + = If roots are real and equal 1 m m = then general solution is
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