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Example 2 Solve the initial value problem y / = x ln x and y(1)=2.

Example 2 Solve the initial value problem y / = x ln x and y(1)=2. Solution By the definition of the indefinite integral all solutions to the differential equation y / = x ln x are given by: Think of x = D ( ½ x 2 ) and integrate by parts:

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Example 2 Solve the initial value problem y / = x ln x and y(1)=2.

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  1. Example 2 Solve the initial value problem y / = xln x and y(1)=2. Solution By the definition of the indefinite integral all solutions to the differential equation y / = xln x are given by: Think of x = D( ½ x2) and integrate by parts: A solution to the initial value problem must also satisfy: Thus the initial value problem has the unique solution

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