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: max value for y

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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,

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

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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:…