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

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1 Point An Equation In The Form Y P Z Y Q Z Y With N 0 1 Is Called A Bernoulli Equation And It Can Be Solved Using 1 (40.3 KiB) Viewed 13 times

(1 point) An equation in the form y' +p(z)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: 1-n v + (1-n)p(x)v = (1-n)q(x) Given the Bernoulli equation we have n SO V = V= V= -32,3 We obtain the equation + Solving the resulting first order linear equation for v we obtain the general solution (with arbitrary con y-y=-ey³ e Then transforming back into the variables a and y and using the initial condition y(0) Finally we obtain the explicit solution of the initial value problem as = 1 to find C C) given by