Question: Please include a step by step solution Problems: Solve the differential equations given below: (show your solution) 1. (x2 + y2 + 1)dx + x(x

Please include a step by step solution

Problems: Solve the differential equations given below: (show your solution) 1. (x2 + y2 + 1)dx + x(x - 2y)dy = 0 (Non-exact Equation) Ans: x2 - y2 + xy -1 = cx 2. y' = x - Zy cot 2x (Linear Equation) Ans: 4y sin 2x = c + sin 2x - 2x cos 2x 3. xdx + sin? () [ydx - xdy] = 0 (Homogeneous Coefficients) Ans: 4x In(=) = 2y - xsin() 4. (y* - 2xy)dx + 3x2dy = 0, when x = 2, y = 1 (Bernoulli's Equation) Ans: x2 = y3(x + 2)

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