questions below:

A differential equation is given along with the eld or problem area in which it arises. Classify it as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear. d 2 y[1+[dZ] ]=C, where C is a constant (brachistoohrone problem, calculus of variations) Classify the given differential equation. Choose the correct answer below. 0 partial differential equation 0 nonlinear ordinary differential equation 0 linear ordinary differential equation The order of the differential equation is (Type a whole number.) The independent l and the dependent Find an integrating factor of the form x"y" and solve the equation. (3xy2 - 4y)dx + (3x2y - 4x) dy = 0 . . . An implicit solution in the form F(x,y) = C is = C, where C is an arbitrary constant, and by multiplying by the integrating factor. (Type an expression using x and y as the variables.) no solutions were lost the solution x = 0 was lost the solution y = 0 was lostUse Euler's method with step size h = 0.2 to approximate the solution to the initial value problem at the points x = 5.2, 5.4, 5.6, and 5.8. 2 y'=;(v2+y).y(5)=3 <:> Complete the table using Euler's method. X" Euler's Method 5.2 |:| 5.4 |:| 5.6 |:| 5.8 |:| (Round to two decimal places as needed.) #mM