Question: Problem solving 1. Write the differential equation e y' + e y = sin x in standard form. 2. Write the differential equation (xy +

Problem solving

1. Write the differential equation e" y' + e" y = sin x in standard form. 2. Write the differential equation (xy + 3) dx + (2x - y' + 1) dy = 0 3. Determine if the following differential equations are linear: a. y' = (sin x)y + e* d. y' + xy' = 0 b. xy' + y = jy e. y' + (x/y) = 0 c. y'+ xy = ey 4. Show that y = Cie" + Caxe" + Cae"* + 2x'e" is a primitive associated with the differential equation; dy dx d'y dy +v = Be. dx dx 5. Determine whether (y - C) = Cx is a solution of the differential equations 4x(dy/dx) + 2x (dy/dx) - y = 0

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