1. (Slope fields) Sketch the slope field to the differential equation dy dr =-y+5 2. (Verify Solution) Verify that the function y(x) = 5-e is a solution to the differential equation dy dx dy dx = y + 5. 3. (Separation of Variables) Use separation of variables to determine the most general solution to the differential equation = sin(x)y.

Q: Consider a differential equation y' = xy + xe¯´.

A: We have y'=xy+xe−x2

Q: Determine the solution of the differential equation: (3tanx - 2cosy)sec²x dx + tan xsin y dy = 0

A:

Q: Solve the differential equation by variation of parameteres:   y'' + y = sin2 (x)

A:

Q: Form the differential equation of family of lines situated at a constant distance p from the origin.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: find the degree of the differential equation y''-12cosec y= 0   3 1 4 or 2

A: The order of the differential equation is 2.

Q: sin x dy (2y Cosx + sin4 x) ax

A:

Q: ind the differential equation of all parabolas whose axis are parallel to the x-axis and have latus…

A: Since equation of parabola whose axis is parallel to the x-axis and have latus rectum a is…