Use Picard's theorem, find the largest interval for which the IVP (x – 8)(x – 1) -y'%3D (x-6)(* +1) y(4) = 0, (x +5)y" %3D x - 3 has a unique solution

Q: Differentiate. y = In [(x + 6)* (x + 7)® (x + 3)5] d [In [(x +6)*(x +7)® (x + 3)°]] = ] dx

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Q: (a) / (2.x4 + Vx3 + 4e* + + 8) dx - (b) / = x3 + 3x – 4 dx - x2 (c) (x + 4)(x³ – 9) dx .3 -

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Q: Integrate S(x-4)(x²-8x+12} dx

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Q: h(x) = 4(2x – 3)*(2x – 5)³ , find h'(x). Factor Fully.

A: Given query is to find the derivative of the expression.

Q: f(x)= (x+2)² (x - 1) f'(x) = 3x(x+2) %3D f"(x) = 6x +6 %3D

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Q: 4x 2 x³ 3 - x²-x+1 S dx.

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Q: y-y1=m(x-x1) y-(-1)=4/5(x-(-1)) y+1 = 4/5x + 4/5 y=

A: The given equation is y+1 = 4/5x+4/5      y = 4/5x+4/5-1         = 4/5x-1/5

Q: (x – 2) tan- (2x) - 12x - 3x (4x + 1)(x – 2)² 39. dx (x + 1)2 tan- (3x) + 9x + x dx (9x? + 1)(x +…

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Q: 40e5*, y(0) = ;, y'(0) =y"(0) 9. y" – 2y" + y' = 2 – 24e* + 2

A: Given: y'''-2y''+y' = 2-24ex+40e5x, y(0) = 12, y'(0)=52, y''(0)=-92

Q: Find 一 az ay -0 if z = (6x + 5y) 7.

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Q: where y1 = e* is one of the functions in the fundamental solution set. - %3D xy" + (2-2x)y' +(x- 2)y…

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Q: y = 5** +(3–x²)

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Q: Differentiate. y = In (4x² - 7x+9) y'=0

A: The function is The aim is to find the derivative of the function

Q: Please help me solve this question

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Q: 1 Show that f (x) = is Libschitz function on %3D x +1

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Q: Suppose X and Y are independent variables such that E[X] = 2, E[Y] = 3, E[X^2] = 9 and E[Y^2] = 15.…

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Q: If f(x) = x²/(1 + x), find f "(1). f"(1) = %3D %3D

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Q: Find all solutions to the equation (D^2 − 3D + 2)y(x) = 2e^3x.

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