(1 point) An equation in the form y' + p(x)y=q(a)y" with n 0, 1 is called a Bernoulli equation and it can be solved usin

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1 Point An Equation In The Form Y P X Y Q A Y With N 0 1 Is Called A Bernoulli Equation And It Can Be Solved Usin 1 (38.21 KiB) Viewed 14 times

(1 point) An equation in the form y' + p(x)y=q(a)y" with n 0, 1 is called a Bernoulli equation and it can be solved using the substitution v= y" which transforms the Bernoulli equation into the following first order linear equation for v: v + (1-n)p(x) v = (1-n)q(x) Given the Bernoulli equation we have n= SO U= y + ²y = ¹²y7 (*) We obtain the equation + v Solving the resulting first order linear equation for v we obtain the general solution (with arbitrary constant C) given by V V= Then transforming back into the variables a and y and using the initial condition y(0) = √3 to find C Finally we obtain the explicit solution of the initial value problem as y =