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Problem: y = arcsin(x) - sqrt(1 - x^2) Find dy/dx Answer Choices: 1/2sqrt(1-x^2) or 2/sqrt(1-x^2) or (1 x)/sqrt(1-x^2) or (x^2)/sqrt(1-x^2) or 1/sqrt(1 x) The arcsin(x) is primarily what is getting me stuck.
To try to solve the problem I moved the root to the other side by adding it to both sides. dy/dx = 1/cos(y) = 1/sqrt(1- (sin(y))^2) = 1/sqrt(1-x^2) because of the trig identity (sin(x))^2 (cos(x))^2 = 1 & because subtracting (sin(y))^2 is the same as subtracting x^2 because of Step One conversion So because I saw the sqrt(1-x^2) in the tougher problem I'm doing right now, I tried to find a way to utilize the technique from the earlier one, but I couldn't.
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res = t*y^2 * yp^3 - y^3 * yp^2 t*(t^2 1)*yp - t^2 * y; This example reformulates a system of ODEs as a fully implicit system of differential algebraic equations (DAEs).