Question: (2) Consider a so-called nonlinear homogeneous first order equation: y? = f(u) where u = y/x. The rest of the questions are on the images

(2) Consider a so-called nonlinear homogeneous first order equation: y? = f(u) where u = y/x.

The rest of the questions are on the images provided. It's parts (a) - (h) I believe.

This is a simple exercise worksheet.

(2) Consider a so-called nonlinear homogeneous first order equation: y? = f(u)

where u = y/x.The rest of the questions are on the images

provided. It's parts (a) - (h) I believe.This is a simple exercise

(2) Consider a socalled nonlinear homogeneous rst order equation: 1;" = f (u) where u = y/m. (a) Determine y in terms of u and 2:. Put the answer in the box provided. y: (b) Determine y' in terms of u, u", and :5. Put the answer in the box provided. (C) Now transform the equation y' = u) into a separable equation it must satisfy. Put the answer in the box provided. 29+ + 2 (d) Solve y' = +3}. provided. Show all your work. Put the answer in the box Other examples! (e) Consider y' = (4a: y + 1)2. What transformation do you see that might be useful? Put the answer in the box provided. (f) Transform the equation! Put the resulting equation in the box provided. @ Hint: y' = 4 u' (g) Solve for u and then y. Put the solutions in the box provided. (h) Now consider (y'(t) )? = t+y. Try to solve it! Hint: When you encounter 1 1 + Vu du try a w-substitution for the denomi- nator

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