Problem 1: Convert the following higher-order ODEs into a system of first ord ODEs (no need to solve the system). You will need to convert the initial conditio as well. [Note that apostrophes are shorthand for derivatives] (a) y"" + 3y" - 2y' + y = 0; y(0) = 2; y'(0) = 1; y"(0) = 3 (b) y" = sin(x); y(0) = 1; y'(0) = 0; y"(0) = 4 (c) (yy')' + y = 0; y(0) = 2; y'(0) = 1

Q: Problem 3 (5V1- x³ ) Find the derivative of y = 6

A: To find the derivative

Q: Find the derivatives of all orders of the functions

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: question 32

A: Given,

Q: Question 8 Find the derivative -[f (x)] dx Anmospace support = 3 In (In (x²-3x + 5)²) 3(2x - 3)…

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Q: 9. If (x-1)/(x) 3x²45x-2 X x²+2x 2x²-x-1 x² g(x) 6x²+x-1 find a relationship between f(x) and g(x).…

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Q: 1, -1 X'=1 3 0 0 2

A: The given differential equation is  dXdt=1-1-1131002X The general solution is of the form…

Q: 1) Graph the function f by starting with the graph of y = x² and using transformations. f(x) =(x –…

A: If f(x)=x2 Now we know that if graph of f(x) is transformed to f(x-a) then we shifts the graph of…

Q: a. f(x) = 2x+9 %3D f-1(x) D %3D b. f(x) = 6x-2 %3D f-(x) = %3D C. f(x) = 3x-5 f-1(x) = d. f(x) = 4-…

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Q: 10. () Give an equation of the tangent line to the graph of the function y = 3r²-2r-11 (it is the…

A: To give an equation of the tangent line to the graph of the function  at the point .

Q: Suppose f, f', g, and g' have the following values: 1 2 3 f(x) 4 - 2 - 2 7 4 f'(x) 9 2 5 - 9 (x)6…

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Q: State the parent function of the equation f(x) = 3Vx +2+1 and the transformations that we applied. 5

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Q: QUESTION 4 State the general anti-derivative of f(x) = -√x F(x) = - 5 x² +C 3 ○ F(x) = -√√x³+C x ) =…

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Q: If s(0)=−4, s(7)=−5, f(0)=2, and s′(x)=f′(x) on [0,7], determine the value of f(7)? (Do not include…

A: We have to determine the value of f7  given,  s0=-4, s7=-5, f0=2 and s'x=f'x on 0,7 Since, s'x=f'x…

Q: If h (x) = (x² – 2x 43 04/0 0 - 12/25 3 00 - (x² – 2x − 1) ³, then h' (0) =? - 43

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Q: 5. A function y = sin x is transformed into = -sin (3x) - 4. What is a possible transformation?

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Q: If all the derivatives of f are defined, and f(3) = 2, ƒ' (3) = −1, f" (3) = 6, ƒ"" (3) = 15 The…

A: Given,

Q: Given f(-19) = -17, g(19) = 13, f'(19) = questions below: a) k(x) = 8f(x) - 4g(x) k'(-19) = b) k(x)…

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Q: 5. +y=ye-² (ve-²) ³ Ans: - e* = ce³x

A: Let us solve the given Ordinary Differential Equation in the next steps.

Q: (a) Compute the derivative of the following functions 8(21)- 21 f(x)= [-x₂+x²³²+x²] ₁+₁²+₁² f(x) =…

A: In this problem, we have been asked to evaluate various properties of two functions f(x) defined…

Q: Problem 4. Find the total derivative of the following function: df dr. af of dy + dr Dy dr F(x,y) =…

A: Sol:-

Q: By using False Position for f(x) = x3 - 4x +4 (XL=-3; xU=2) xr will replace

A: This is interesting question but before the solution we must know about the  false position method…

Q: If f(x) = csc(3x). then f' (x) = %3D o -3csc(3x)cot(3x) o -3csc2 (3x) o 3sec(3x)tan(3x) o 3tan? (3x)

A: Given: fx=csc3x To evaluate: f'(x)