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**Unformatted text preview: **11. In this problem, the independent variable is t and the dependent variable is x ; f ( t, x ) = 1+ x 2 , t = 0, and x = 0. The function ( t ) = tan t satises the initial condition: (0) = tan 0 = 0. The diFerential equation is also satised: d dt = sec 2 t = 1 + tan 2 t = 1 + ( t ) 2 . Therefore, ( t ) is the solution to the given initial value problem. 22...

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