Solve the initial value problem x' 8. -1 x, х(0) 4 1 Describe the behavior of the solution as t → 0o. -4 x = Choose one Choo Choose one 28 1 5 8 – 7t 1 e2t (); 8 e7t 1 2t #()-*-(;)~* 28 -2t 5 28 1 e2t 6 - --

Q: Find the artied mainly do the Чтоза g(x) = 4x6 e

A: To find the critical points for the given function

Q: Solve. x- - Sx - 7> 0 O (, -7) U (-1, o) O (1. ) O (, -7) O +7, -1)

A: It is given that,x2+8x+7>0 We have to solve it.

Q: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

Q: Solve for X. X = 1 1 -8 7 8 [6 8 43-64-4 X = I.

A: The addition and subtraction of two matrices A and B are defined only if A Nad B have same order.…

Q: The characteristic equation associated with x" + 19x' - 27x = 0 is Select the correct response: m2 +…

A: Given:- x''+19x'-27x=0 To find :- Characteristic equation of given differential equation

Q: 1) The distance, travelled by a car, f(x), in meters, after x hours, can be represented by f(x + 20,…

A: Disclaimer: Since you have asked multiple question, we will solve the first question for you. If you…

Q: 14. If MZSTU = (5x – 16)' and mSU = (12r – 50) , find MZSTU.

A: Given,       m∠STU=5x-16°   and   m SU⏜=12x-50°

Q: Solve for the 2"nd derivative of the function f (x) = 3x5 – 4x3 + 7x² – 10. a. 15x* – 12x2 + 14x b.…

A: Given: fx=3x5-4x3+7x2-10 To Find: 2nd derivative of the given function

Q: A new flag pole for a school campus measured 25 2/3 feet. It was put 4 1/2 feet into the ground and…

A:

Q: Solve the initial value problem If the solution is v=Σακ*, k-0 enter the following coefficients: Go=…

A: Let the solution of  be

Q: Find f'(x) and simplify. X + 8 f(x) = Зх — 4 (x² + 8) O A. (3) - (3х - 4)(2x) [3х - 4)2 (3x – 4)(2x)…

A:

Q: Differentiate y = 2sin? (x³) + 3x and evaluate y (0). Enter the value y (0) in the box and upload…

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Q: 5.Jf(x) =- 3x + 7 g(x) = 2x - 8 Find f(g(x))

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Q: s2+9s+2 L-1(, -) = 2e-t + 3teAt – e-3t (s–1) (s+3)) = 2e¬t + 3teAt ,

A:

Q: 7x2 + 6x + 2 If f(x) then: f'(x) = f'(2) =

A: The given function is f(x)=7x2+6x+2x

Q: x?S(x x] =0 2 2 x Can be wpitden as s" (o)= the Solu tion is

A: Note:- You have mistakenly written it as c1e^ax + c2e^-ax. At the place of a there will be α.

Q: 11. (4g³h)(-2g³) 12. (–15xy* )(- { xy*) 13. (금p)"

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Q: 12. Solve for x. 120 (Sr + 21)'

A: To find :                  Solve for x

Q: Refer to the figure below. Find a - b + c. x' - (, :)x+ () 3 X' = X + 3 ; X(0) = (;) 4e4t Answer : X…

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Q: Find f (x) and simplify. x +5 f(x) = Зx-2 Which of the following shows the correct application of…

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Q: If '(3) = -1 and h'(1) = 5, then "(r)dr= (A) -6 (B) 4 (C) 5 (D) 6 (E) 9 (F) 11

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Q: + B O Use un determined coefficients to find a particular Solution to x' = 2x + 3y +5, g` = 2x+y -…

A: Step 1:To find the solution to the given system of differential equations using the undetermined…

Q: a. || 8 3)++ (-2) x+ t> 0

A:

Q: Find g' (3) given that f(3) - 5 andf' (3) Enter the exact answers. (a) g(x) = 4x² – 3f(x) g' (3) = i…

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Q: (2k

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Q: If u(x) = x3, then du = 3x2.

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Q: If f(x)=5x-1, g(0)=2, g'(0)=4, and h(x)=f(g(x)), then what is h'(0)?

A: Given that h(x)=f(g(x)) Using chain rule we get: h'(x)= f'(g(x))g'(x) We plug x=0 So, h'(0)=…

Q: Solve the following ODE y +2Y +y=x + ex (C1 + x C2) e* + (x-2) + e²x / 9 .a O (C1 + x C2) e* -2 +…

A:

Q: find the longest interval in which the following initial value problem is guaranteed to have a…

A: Consider the initial value problem    y"+P(x)y'+Q(x)y=g(x)y''(x0)=a                 y'(x0)=b If…

Q: which one is y=g(x), y =g'(x), y=g''(x), y=g'''(x)

A: We have to fund which graph corresponds to g(x),g'(x),g''(x),g'''(x)

Q: Find the Derivative

A: The derivative of a function with respect to a variable is equal to the instantaneous rate of change…

Q: Find h(x) if h'(x)= h(x): 5x (6-x²)² X and h(1) = -6.

A: NOTE: Refresh your page if you can't see any equations. . here we have take integration on both…

Q: If f(x) = V5x – 3, find f-1(x). | 3 x3 + 3 А. f-(x) C. f-1(x) : ==X- 5° 3 3 x3 f-(x) =- f-'(x) = 5…

A: Given, f(x)=5x-33 To find the inverse function, f-1(x) Take f(x)=y . The idea is to solve the above…

Q: I. Solve for the unknown/s. 1. x:4 = (2x + 3) = 12 2. (x+ 1): (2x + 3) = (x + 3)(2x + 8) 3. (3x –…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.