Find y as a function of a if y" - 14y" +48y' = 70e", y(0) = 12, y'(0) = 29, y" (0) = 28. y(x) = 7.84+ (4.02)e^(6x) -(1.86) e^(8x) + 2e^x

Q: Find f'(1) for f(x) = ln(3x² – 6x – 2) rounded to 3 decimal places. f'(1) = |6-6x/3x^2-6x-2

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Q: Find f.   f ''(x) = (5/6)x5/6

A: Consider f''x = 56x56

Q: Find y=f(x), if f''(x)=3x^2, f'(0)=-7 and f(0)=2.

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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: Find y'' in y = x(2x + 1)4

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Q: Find f. f"(x)  =-2  +12 x -12 x2   , f(0)   = 4 ,f'(0)  =12

A: Given ,f''x=-2+12x-12x2f0=4f'0=12

Q: if y= (1+e^x)X^3 then find y`

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Q: Calculate y" and y"". y(x)= y" (x) = y"" (x) = 10e*

A: The given function is

Q: Find g’(t) for the function g(t)=5/t^3

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Q: 3. y' = 3x? –2; y(1) = 5

A: When the linear differential equation is in the form, dydx+py=Q    ..........1 Then the solution of…

Q: Find f'(x), f'"(x), and f""(x). f(x) = 4x? (2– 9x -3) f'(x)= f'"(x) =|

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Q: Find f. f ''(x) = −2 + 36x − 12x2,    f(0) = 3,    f '(0) = 16

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Q: Find y'' in y = (1 - √x)-1

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Q: if y= 1/2x^3 then find y`(0.50)

A: We find y' or first derivative of y using power rule. d/dx(x^n)= n*x^(n-1)

Q: xy' = 3y + 8x, y(2) = 8. y= ((8x^8/8)+3)x^3

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Q: For each of the following y, find the d^2y/dx^2

A: We know, d/dx (xn)= nxn-1, for any real number n. d/dx(u(x)v(x))= v(x)*d/dx(u(x))+u(x)*d/dx(v(x))

Q: Find y''' for y = 1/(x+4)3

A: To find the first derivative, y' of y, differentiate (x+4)-3 with respect to x, using the general…

Q: Find y as a function of x if y" +81y' = 0, y(0) = 4, y'(0) = -27, y"(0) = 81. %3D |

A: Given that y’’’ = 81y’ = 0 And y(0) = 4, y’(0) = -27, y’’(0) = 81 y(x) = ? y’’’ = 81y’ = 0 let d/dx…

Q: x 3y'''- x 2y'' + 2xy' - 2y = x3

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Q: Evaluate y''' or d^3y/dx^3 of the function (1/3)x^3 + (1/3)y^3 = (1/3)^2  when x = 0

A: Given, 13x3+13y3=132.   The objective is to find y''' at x=0.   Now, 13x3+13y3=132y=91-3x333

Q: For y=f(x)=3x^3 , x=3 , and (triangle)x = 0.03 find dy (two decimal places)

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Q: Find y=f(x) if f''(x)=4x^2, f'(0)=3, and f(0)=2.

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Q: 6) find the 2nd derivative and the graph Y’= 12-x-x^2

A: y'=12-x-x^2 Differentiate with respect to x, we get y"=-2x-1 Graph using desmos,  1) Graph of -2x-1…

Q: Find f. f ''(x) = −2 + 30x − 12x2,    f(0) = 4,    f '(0) = 16   f(x) =

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