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1)Consider the following initial-value problem. (x + y)2 dx + (2xy + x2 − 2) dy...

1)Consider the following initial-value problem.

(x + y)2 dx + (2xy + x2 − 2) dy = 0,   y(1) = 1. Let af/ax = (x + y)2 = x2 + 2xy + y2. Integrate each term of this partial derivative with respect to x, letting

h(y) be an unknown function in y.

f(x, y) =   + h(y)

Solve the given initial-value problem.

2) Solve the given initial-value problem.

(6y + 2t − 3) dt + (8y + 6t − 1) dy = 0,    y(−1) = 2

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