Given a differential equation of the form dy dt = g y t ,

Chapter , Problem 16

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Given a differential equation of the form dy dt = g y t , show that the change of variables u = y/t gives a separable equation for du/dt. (First-order differential equations of this type are sometimes called homogeneous. This use of the term homogeneous is not the same as its use with linear equations as in Section 1.8.)

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