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

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An Equation In The Form Y P X Y Q X Y With N 0 1 Is Called A Bernoulli Equation And It Can Be Solved Using The Subs 1 (38.46 KiB) Viewed 13 times

An equation in the form y' + p(x)y=q(x)y" with n 0, 1 is called a Bernoulli equation and it can be solved using the substitution v= y¹n 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(z) Given the Bernoulli equation we have n = SO V = V= 3 y +=y=! We obtain the equation + Solving the resulting first order linear equation for v we obtain the general solution (with arbitrary constant C) given by V= 9ay 3 Y (*) Then transforming back into the variables and y and using the initial condition (1) = 1 to find C= Finally we obtain the explicit solution of the initial value problem as