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dy + p(t)y = g(t)y". dt (a) This equation is nonlinear which seems hard to solve. However, show that the sub- stitution v = y¹-n transforms the given differential equation into a linear differential equation in v. (b). Find the solution y(t) of the original differential equation.

dy + p(t)y = g(t)y". dt (a) This equation is nonlinear which seems hard to solve. However, show that the sub- stitution v = y¹-n transforms the given differential equation into a linear differential equation in v. (b). Find the solution y(t) of the original differential equation.

Calculus For The Life Sciences
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 5E
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dy + p(t)y = g(t)y". dt (a) This equation is nonlinear which seems hard to solve. However, show that the sub- stitution v = y¹-n transforms the given differential equation into a linear differential equation in v. (b). Find the solution y(t) of the original differential equation.
Transcribed Image Text:dy + p(t)y = g(t)y". dt (a) This equation is nonlinear which seems hard to solve. However, show that the sub- stitution v = y¹-n transforms the given differential equation into a linear differential equation in v. (b). Find the solution y(t) of the original differential equation.
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