(a) Consider the differential equation y’=1/(x+1) Determine a region R in the xy

| August 31, 2017

uestion
(a) Consider the differential equation y’=1/(x+1) Determine a region R in the xy plane for which the differential equation would have a unique solution through a point (X0, Y0) in R. (b) Show that y=ln(x+1) satisfies the differential equation and the condition y(0)=0, but explain why y=ln(x+1) is not a solution of the initial value problem y’=1/(x+1), y(0)=0 on the interval (-2,2). (c). Determine the larges interval of validity for which y=ln(x+1) is a solution of the initial value problem in part (b).

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