Given the differential equation: (4xy + 3y² - x) dx + x(x + 2y)dy = 0 The solution to the differential equation: (4xy + 3y² - x) dx + x(x + 2y)dy = 0 may be expressed in the form xa (bxy + byc + dx) = e Find: a + b +c-d+e. when x = = 1, y = 2

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A: To solve for the value of constant C in  the equation: 2x+3y'=y+2x+312when x=-1, and y=0.

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A: Here we can create the required polynomial function in the below steps.

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A: Topic- Derivative of a function  We are given, f(x)=4x2tan xsec xand f'(x)=4x(x+2tan (x))sec x

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A: This question can be solved using the concept of limits.

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A: SOLUTION-

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A: NOTE: Refresh your page if you can't see any equations. . compare this DE with   so here we have

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A: Solve by derivatives

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Q: 5 5 Suppose ff(x) dx = 25, f f(x)dx s., $ f(x)d. 3 0 the following: a. 0 3 (5f(x) - 6g(x) + 4h(x))dx…

A: The basics of integration must be cleared in order to attempt this question. Rest of things are…

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A: solution:-y=9x2-1slope= dydx=ddx9x2-1=18x(a)slope of tangent at point P(4, 143)slope = 18(4)=72

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