Question: 1. Find the partial derivative (a) wrt x and (b) wrty 1. x2 + 5xy -y3 = 0 2. x2y4 - 3xy2 + 5y=7 3.

1. Find the partial derivative (a) wrt x and (b) wrty 1. x2 + 5xy -y3 = 0 2. x2y4 - 3xy2 + 5y=7 3. y sin x + x2tan y - xy* = 0 II. Determine the homogeneity of a given function. 1. f(x,y) = 4x2 -3xy +y2 2. f(x,y) = x In x - xIn y 3. f(x,y) = x-+3xy x-y III. Solve the DE: 3 (3x2 + y2) dx - 2xydy = 0 IV. Find the general solution of the differential equation: (x+y) dx + (x-y) dy =0 V. Find the particular solution of the DE: (y'+7xy + x2)dx +x-dy = 0, with an initial condition of x=1 and y=1

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