(1 point) A Bernoulli differential equation is one of the form Consider the initial value problem = Observe that, if n =

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1 Point A Bernoulli Differential Equation Is One Of The Form Consider The Initial Value Problem Observe That If N 1 (28.06 KiB) Viewed 48 times

(1 point) A Bernoulli differential equation is one of the form Consider the initial value problem = Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution uyl transforms the Bernoulli equation into the linear equation 7 = (b) The substitution" = 비 (a) This differential equation can be written in the form (*) with P(x) = Q(x) = du dx and dy dx du dx u= (e) Finally, solve for y. y(x) = + P(x)y= Q(x)y (+) +(1-n)P(x)u= (1-n)Q(x). xy + y = -5xy, y(1) = 1. will transform it into the linear equation (c) Using the substitution in part (b), we rewrite the initial condition in terms of x and u: u(1) = (d) Now solve the linear equation in part (b), and find the solution that satisfies the initial condition in part (c). u(x) =