and (2) and (3) of this section. dy = f(x, y) dx Solve: (2) Subject to: y(x) = Yo d?y - f(x, y, y') dx2 Solve: (3) Subject to: v(x,) - YouY'(xo) = Y1 Find a function whose second derivative is y" = 12x – 2 at each point (x, y) on its graph and y = -x + 8 is tangent to the graph at the point corresponding to x = 1.

Q: Find y as a function of a if y(0) = 7, y'(0) = 4, y"(0) = 133. y(x) = y" - 8y" -y + 8y = 0,

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Q: 2 a) For the function f(x) = X-3 , find f'(1) by using the definition of derivative.

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Q: Find y' and y". In(7x) y = x7 y' = y" %3D

A: The given function is: y=ln(7x)x7 Therefore, y'=1x7ddx(ln(7x))+ln(7x)ddx1x7    =1x717x·7+ln(7x)-7x8…

Q: 2) A function is given by 00 x* e=*dx. *e*dx. h(k) 00 Its values may be found in tables. Make the…

A: Recall that the Gamma function is an alternate form for defining the factorial notation. Gamma…

Q: 4 Use implicit differentiation to solve for y' if r4y2 - x³y + 2xy³ = (Show your work)

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Q: Given xy + 2x + 3x² = 1: (a) Find y' by implicit differentiation (leave your answer in terms of x…

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Q: Find f'(2) if y = f(x) is the nonnegative function defined for x, y > 0 by the equation x" = y?.

A: To find f’ (2), if y = f (x).

Q: Find any relative maxima and relative minima. relative maximum (x, y) = relative minimum (x, y): %3D…

A: The given function is - y = x(x-5)2y' = -x+5(x-5)3y'' = 2x+20(x-5)4

Q: 3y' –4x²y+ xy = -5 %3D

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.