Consider the initial value problemA Bernoulli differential equation is one of the formObserve that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y¹n transforms the Bernoulli equation into the linearequationn =(a) This differential equation can be written in the form (*) withP(x) =Q(x) =(b) The substitution u =dud.x+and(e) Finally, solve for y.y(x)=dud.xU =dydx+ P(x)y= Q(x)y" (*)+ (1 − n)P(x)u = (1 − n)Q(x).xy' + y = −8xy², y(1) = −7.(c) Using the substitution in part (b), we rewrite the initial condition in terms of x and u:u(1) =| =will transform it into the linear equation(d) Now solve the linear equation in part (b), and find the solution that satisfies the initial condition in part (c).u(x) =

Answered: Image /qna-images/answer/60af9230-6c9e-4fd6-b5ba-d4fc6995e371.jpg

Consider the initial value problem A Bernoulli differential equation is one of the form Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y¹n transforms the Bernoulli equation into the linear equation n = (a) This differential equation can be written in the form (*) with P(x) = Q(x) + = (b) The substitution u = du dx = and du dx U = (e) Finally, solve for y. y(x) = dy dx + P(x)y Q(x)y" (*) + (1 − n)P(x)u = (1 − n)Q(x). xy' + y = −8xy², y(1) = −7. (c) Using the substitution in part (b), we rewrite the initial condition in terms of x and u: u(1) will transform it into the linear equation (d) Now solve the linear equation in part (b), and find the solution that satisfies the initial condition in part (c). u(x) =

Consider the initial value problem A Bernoulli differential equation is one of the form Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y¹n transforms the Bernoulli equation into the linear equation n = (a) This differential equation can be written in the form () with P(x) = Q(x) + = (b) The substitution u = du dx = and du dx U = (e) Finally, solve for y. y(x) = dy dx + P(x)y Q(x)y" () + (1 − n)P(x)u = (1 − n)Q(x). xy' + y = −8xy², y(1) = −7. (c) Using the substitution in part (b), we rewrite the initial condition in terms of x and u: u(1) will transform it into the linear equation (d) Now solve the linear equation in part (b), and find the solution that satisfies the initial condition in part (c). u(x) =

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...

See similar textbooks