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okay in this video were gonna look at a very important and useful result in differential equations known as Abels theorem so it says the following so lets suppose that y1 and y2 are linearly independent solutions of this second-order linear homogeneous differential equation given by y double prime plus P of X times y prime plus Q of X times y equals 0 on a and B so these are solutions on the interval a B where P of X and Q of X are continuous on the interval a B so were going to set W equal to the wronskian of y1 and y2 in other words its the determinant of this following matrix column Y is defined by y 1 y 1 prime y 2 y 2 prime then we know that W of X is equal to W evaluated at X naught and then the exponential of negative the antiderivative of this function P where weve taken this kind of formal antiderivative as the definite integral from a point X naught to X of P of T DT and it turns out that X naught can be taken to be any number in a and B so it follows from this that th
