A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point (a, b), then at least one so- lution of the differential equation y = f(x, y) exists on some open interval I containing the point x = a and, moreover, that if in addition the partial derivative af/ay is continuous near (a, b), then this solution is unique on some (perhaps smaller) interval J. In Problem determine whether ex- istence of at least one solution of the grven initial value prob- lem is thereby guaranteed and, if so, whether uniqueness of that solution is guaranteed. dy = x2 – y2: y(0) = 1 dx

A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point (a, b), then at least one so- lution of the differential equation y = f(x, y) exists on some open interval I containing the point x = a and, moreover, that if in addition the partial derivative af/ay is continuous near (a, b), then this solution is unique on some (perhaps smaller) interval J. In Problem determine whether ex- istence of at least one solution of the grven initial value prob- lem is thereby guaranteed and, if so, whether uniqueness of that solution is guaranteed. dy = x2 – y2: y(0) = 1 dx

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,...

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