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

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1 Point An Equation In The Form Y P X Y G X Y With N 0 1 Is Called A Bernoulli Equation And It Can Be Solved 1 (61.41 KiB) Viewed 9 times

(1 point) An equation in the form y' + p(x)y = g(x)y" with n # 0, 1 is called a Bernoulli equation and it can be solved using the substitution v = y¹ 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 -5 SO V = We obtain the equation + 16 y^6 V= y' + ² y = 10 e ¹²y=5 (*) Solving the resulting first order linear equation for v we obtain the general solution (with arbitrary constant C) given by V= Then transforming back into the variables x and y and using the initial condition y(0) V1 to find C = Finally we obtain the explicit solution of the initial value problem as y = -n which transforms