Please do both question 6 and 7 with full solutions so i can learn.

see attached image for full question.

Question 6: Determine whether the differential equation 2xy' - y = 2x5/2 cos x is: - separable or non-separable? - linear or nonlinear? - if linear, specify whether it is homogeneous or non-homogeneous? Give reason for each your answer to these questions Find a particular solution for x > 0 subject to the initial condition y( ) = JR . Substitute the solution derived into the differential equation and confirm that it satisfies the equation. Question 7: a) Determine the type of the differential equation (x2 +1) y' -1=-4xy (is it linearonlinear, separableon-separable, homogeneouson-homogeneous)? b) Find a particular solutions subject to the initial condition y(-1) = -1/3. c) Determine, whether this function is odd, even, or neither odd nor even; give reason (for definitions of odd and even functions : d) Plot the solution in the interval x e [0, 10]. You can use either any technology or a simple calculator (there are several graphical calculators in the Internet)