EXERCISE 1.2. Obtain a partial differential equation from each of the following relations: (a) 2z =...

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EXERCISE 1.2. Obtain a partial differential equation from each of the following relations: (a) 2z = (ax + y)² + b (b) ax² + by² + cz² = 1 (c) z = (x + √x²-a²)y + b (d) z = (x² + a)(y² - b) (e) f(xy + z²) = x+y+z (f) f (z sin x, z cos y) = 0 (g) z = μ(y-ax) + 8(y-bx) EXERCISE 1.2. Obtain a partial differential equation from each of the following relations: (a) 2z = (ax + y)² + b (b) ax² + by² + cz² = 1 (c) z = (x + √x²-a²)y + b (d) z = (x² + a)(y² - b) (e) f(xy + z²) = x+y+z (f) f (z sin x, z cos y) = 0 (g) z = μ(y-ax) + 8(y-bx)