(a) Find the general solution of the differential equation dx = x – x2 dt (b) Solve the following first-order ODE xy'y=2x* +2y* You are required to provide each step clearly.

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A: Trapezoid rule

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A: Topic:- application of derivatives

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A: We will find the derivative of the given function in the following step.

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A: Solving

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A: Explained below

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A: We can solve question no 5 and 6 using chain rule as below.

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A: We can find the dot product as below.

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A: The detailed solution is given below Thank you

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A: As per guidelines we have to solve one question Please repost other questions again

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A: Use the method of substitution and solve the integration.

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A: Given query is to find the the interval where function is concave upward and downward.

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A: To find out dw/dt.

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