SPECIALIZATIONSIN DIFFERENTIAL ALGEBRA Ams Form

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how would you solve an equation that looks like that y double prime minus five y prime plus six y is equal to zero how would you solve that differential equation in this video we're going to talk about it but first you may want to have a sheet of paper with you to take down some notes so we're going to talk about how to solve second order linear differential equations now these type of equations are usually in this form where p of x q of x and r of x are continuous functions now when g of x is equal to zero what we have is a homogeneous linear equation if g of x equals some other number if it doesn't equal zero then we have a non homogeneous equation now when p q and r are constant functions we have this equation a y prime plus b y prime plus y equals i mean plus c y rather equals zero and a typical solution of this equation is in the form y is equal to e to the rx if you take the first derivative of that you're going to get r e to the rx and if you take the second derivative of that y