(1 point) An equation in the form y' + p(x)y=q(z)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 Z Y With N 0 1 Is Called A Bernoulli Equation And It Can Be Solved Usin 1 (38.54 KiB) Viewed 15 times

(1 point) An equation in the form y' + p(x)y=q(z)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(z) Given the Bernoulli equation we have n We obtain the equation SO V= + Solving the resulting first order linear equation for v we obtain the general solution (with arbitrary constant C) given by V= y + ly=e4y3 Then transforming back into the variables a and y and using the initial condition y(0) 3¹/4 to find C= Finally we obtain the explicit solution of the initial value problem as Y