The initial value problem has a unique solution defined on the interval Type -inf for - and inf for +∞ (t²-25) y" - 5ty' +9y= ln (t²) y(-4)= 5 y'(-4)=9

Q: y''' -3y'' + 3y' -y = (e^x)(x+1) find the general solutions of this diff eq

A: Given differential equation is y'''−3y''+3y'−y=exx+1 Write the auxiliary equation  m3−3m2+3m−1=0…

Q: max value for y

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Q: (x^2)y'' - xy' + y=x*(lnx)^1/2 find the general solution of this diff eq

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Q: If y = (4x + 7), find y' (1). O 11 ln(11) + 4 O 11 ln(11) O - O 11 ln(11) - 4 In(11) – - In(11) + 4…

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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: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

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Q: If R'(x)=250-18x and R(0)=0, find R(x)

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Q: 1. Find f'(x) for f(x) = ln x + 2e - 3x².

A: The given function fx=ln x+2ex-3x2. We have to find the derivative function f'x.

Q: solve  w' + ((2w)/x) = x5,       w(0) = 1 what is w(1)

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Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: Solve Where X (0) = (1) 1 = (-²₂23) X(0) + (₂) X' (t) =

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Q: if f(x) = x² √In x² x . find the derivative of this function f'(x A. f'(x) = B. f'(x) = c. f'(x) =…

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Q: .) The instantaneous rateof change fucntion of f(x) = 4x² - 2x + 8 or the derivative of f(x) is: a.…

A: Given that: (i) f(x)=4x2-2x+8(ii)f(x)=sin x

Q: Longest interval for (t+2)y’’-(sint)y’+ty/t-4=e^2t/t y(-1)=0

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Q: Find yy as a function of x if y′′′−7y′′+12y′=6e^x y(0)=30,  y′(0)=19,  y′′(0)=12

A: y′′′−7y′′+12y′=6ex        y(0)=30,  y′(0)=19,  y′′(0)=12 given differential equations is linear…

Q: A developing country's gross domestic product (GDP) from 2006 to 2015 is approximated by the…

A: Given: The GDP of a country is given using the function: Gt=-0.3t3+3.6t2+54 (a) Firstly find the…

Q: Ex. 8 Differentiate k(x)= ln(x)f(x)

A: Our AIm is to differentiate the function given below:-f(x)=ln (x) f(x) -(i)

Q: Given f''(x)=9x+0 and f'(0)=−3 and f(0)=4.   Find f'(x)=     and find

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Q: if f(x) = %79.1 x²√In x² x -. find the derivative of this function f'(x) A. f'(x) = - 1 3:16 1-In x²…

A: The given function is; f(x)=x2 sqrt(ln x2)/x.

Q: Given f’(x) = 5cosx-16sinx    and f(0)= -1   Find f(x)

A: f’(x) = 5cosx-16sinx  We need to obtain the integral of this and satisfy the boundary condition.…

Q: y""+12y" +36y=0; y (0) = 0; y'(0) = 1;y" (0) = -7 ✓y""+y" - 2y=0 y" - 4y'-5y=0; y ( 1) = 0; y' (1)=2…

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Q: If g(x) = , what is g'(x)? 2x-1 x²+3x '

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Q: Suppose y(t) = c1 e^(-t) [1 -1] c2 e^(t) [ 1 1], with the initial condition y(1) = [0 2]. Find c1…

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Q: The derivative of f(x) = 9z3 12 8. is %3D 3z f'(x) O f(r) – 9x?+ 12x 4 – 9r– 12x + 8e 7 O f(r) - 9x…

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Q: Find g' (6) given that f(6) = - 3 and f' (6) = 6. Enter the exact answers. (a) g(x) = 7x² – 6f (x)…

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Q: f f(x) = x²√Inx² x . find the derivative of this function f'(x) 1-In x² x²√√In x² A. f'(x) = B.…

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Q: y' = 8|x| = - 8x, x≤0 8x, x>0

A: To find y'' and graph the general shape of f(x), we first need to integrate the given expression for…

Q: 3. What is the FIRST derivative of the given function? y = 3x³ - 2x² + x - √√2

A: Given,            y=3x3-2x2+x-2To find : What is the first derivative of the given function.

Q: Find g'(4) given that f(4) = -3, f'(4) = -8, and g(x) = √af(x)

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Q: 23. If f(x)= 3x2+2x+1, find f'(2) O 6x+2 O 14+3x O 14 O 2x+1

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Q: If y = (3x+8)x, compute y'(1). y'(1) = X

A: We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x The Product rule:…