Derive the expression  F1− F2 = (F1 − Fc)exp( f φ) − 1/exp( f φ) using the equation (F1− Fc/F2− Fc)= exp( f φ)

Q: let f(x) = 2x^2+2x+3 and let q(h) = f(1+h) - f(1)/ h.    Then q(0.02) = ?

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Q: Let f(x) = x³ – 2x – 6. Tell why f has a solution in [1, 3], and use the Newton-Raphson method with…

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Q: Find an explicit form of the general solution of the following ODE: (x – 1) y" + 2y' = 0.

A: Given

Q: f (x+2) In (x+2) - 4 tc (x+2) Xt *+ 2

A:

Q: Solve the following ODE 3 y' + • y = 0 with initial condition y(1) = 2 -

A: Write y'=dy/dx and then use variable separation.

Q: 3 Q.19: Find f(x) = 3x2 + 3x +1 for A = 1 2 1 [2 1 o]

A: Here A=163121210So,A2=163121210163121210A2=1321951153147

Q: Find (f=1)'(a). f(x) = 5 + x2 + tan(Tx/2), -1 < x < 1, a = 5 (F-1)'(a) =

A: NOTE: Refresh your page if you can't see any equations. . take x=0 and check  so the point…

Q: Generate the approximation formula 1 f'(x) × - [4f(x+ h) – 3f(x) – f(x+2h)] 2h with the error term.

A: The objective is to generate the approximation formula,

Q: Ex/ show that f(x) = x+7x + 4 x + 1 has an inverse. %3D

A: In this question we have to find whether the function has an inverse.

Q: (a) f(x) = (2x – 1)*(3x – 2)³ (b) f(x) = [(x – 3)(5x + 1)]³ (c) f(x) = Vx cos ((3x + 2)²) %3D CoS…

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Q: 5. If f(x) = 2x² - 3 and g(x) = 2 sinx, determine (fog)(x) and (fog) (), 0≤x≤ 2n.

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Q: Find for f'(x) | f(x) = x – cos(x) f(x) = e* – 2x - 2

A: To find f'(x).

Q: Find (e3x + 5sinx)dx. -e3x +5cosx +C O a. 3 e3x+1 -5cosx + C b. 3x + 1 e3x -5 cosx + C OC. -e3x -…

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Q: Find the general solution of the given ODE.

A: Given differential equation is y'=1+x1+y2dydx=1+x1+y2dy1+y2=1+xdx

Q: The general solution for the ODE -2y+y

A: The correct answer is option c  and the solution follows as

Q: Find De f Re ー X - 2 2SXミ-1 y = P(x) = ーX+2

A: The domain of a function f(x) is the set of all values of x at which the function is defined i. e…

Q: 2=Cメて+x -x2 Using Cramer's Rule メメt10n- 3xx=5 %3D

A: Solution using Cramer's rule is given as follows :

Q: xy' + y = Vx %3D

A: Introduction: A first-order linear equation is of the shape y'+p(x)y=q(x). The integration issue of…

Q: 2x + 3 f(x) = In %3D 7r – 7 f'(x) =

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Q: 59. (а) у 3 f(x) + 1 (b) у -- fo) - 1 (e) y = 25) y =f(x) (-1, 2) (0,0) (-2, 0) (2, 0) Ia.-2)

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Q: f(t) = Vt - 4

A: Given: f(t)=t−43

Q: Example 13: If Jf(x)dx =-3, )dr=9, and f(x)dx 5, find %3D

A: given∫4-6f(x)dx=-3,∫37f(x)dx=9∫47f(x)dx=5to find∫-63f(x)2-3dx

Q: Find f(2) given that f(z) = 2r +5.

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Q: e 2t * – 3x + 2x = e2t+1

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Q: When f′(x0f′(x0) =0, then Newton-Raphson method fails.

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Q: Find the general solution of the given ODE x+1 v +1

A: dydx=x+1y4+1 (y4+1)dy=(x+1)dx Integrate both sides ∫(y4+1)dy=∫(x+1)dx∫y4 dy + ∫dy  = ∫x dx + ∫dxy55…

Q: 1°- 4+ 4r2 -4 dr Co T. (1²-1)(r²+2r+2)

A: Indefinite integration is the backward process of differentiation. Through integration, we find a…

Q: Suppose that f(4) = 2 and f' (4) = h(x) = (2x² + 3in (f(x)))² h' (4) = (b) h(x) = 20f(x) e-2x + 3…

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Q: Find each f(c) using synthetic substitution. 12. Ax) =5x + 10x* + 3x + 8x² – 6x – 3; c = 3 (SHOW…

A: Concept - we have given a function F(x) , and asking about C=3 ,so substitute c in given…

Q: Suppose that f(4) = 2 and f' (4) = -1. (a) h(x) = (2x². 2x² + 31n (f(x)) h'(4) = (b) h(x) = 20f(x)…

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Q: Find (f-1)'(a). TX f(x) = 8 + x2 tan 2 -1 < x < 1, a = 8 %3D (f-1)'(a) =

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Q: 1) Show that (a) y =xe satisfies the eq. xy' (1-x)y (b) y =xe"A satisfies the eq. xy'=(1-x²)y

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Q: Suppose that f(x) 16e" – exº. Find f'(3). f'(3) =

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Q: Solve the DE f'(x) = 5x given that f(0) = 3. %3D

A: The objective of the question is solve the  DE with help of given conditions.

Q: 1. Determine the exact value of sec- л 4 1 √√3 B. √2 ~ C. √2 1⁄23

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

Q: 3-4 3. - find A-! L i As

A: Given query is to find the inverse matrix.

Q: 2 In x 1 e* 2 1 In 2x -1

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Q: Determine c1 and c2 so that y(x) = c1 e^2x + c2 e^x + 2sin x will satisfy the conditions y(0) = 0…

A: NOTE: Refresh your page if you can't see any equations. . the given solution is…

Q: 3 a. f(x) = V3x³ – 2 - b. y = (vx + 1)(x² – x) 2x5-3 c. f (x) coS x

A: a) fx=3x3-23b) y=x+1x2-xc) fx=2x5-3cosx Note:   Multiple parts are given, we are answer only three…

Q: Solve cotx+ 3-0 on the interval x e [0,21]. O a) 6. 11x X3D O b) x-x-5 X = Od4- c) X = 11T 元 d x=…

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Q: Show that So e-ax J₁ (bx) dx= 1 √(a³ + b³)³ (a > 0)

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Q: Find (f-1)' (a)   f(x)  = x3 + 3Sin x  + 2Cos x  , a= 2

A: Given expression: fx=x3+3sinx+2cosx Differentiate the above expression w.r.t 'x'…

Q: Find f(3-2i) when f(t)=t^2 -3t -5 write the result in the form a+bi

A: Explanation of the solution is given below...

Q: bah ow )o (d) be . Solve for 0<x <1, u"- u =-f(x) u' (0) = u' (1) = 0.

A: As f(x) is an arbitrary function, we will use Green's function to find the general solution.

Q: af 8. Find and ax of f(x, y) = e-* sin (x + y) ду

A: A detailed solution is given below.

Q: 3. Consider the linear ODE: -2 -1 1 + %3D 1 find the general solution

A: given linear ODE dx1dtdx2dt=-2-101x1x2+11 claim- find the general solution

Q: ) Differentiate:  (a) f(x) = √x(cos)x2 (b) f(x) = 2x/x2 + 4

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Q: Find the general solution of the given ODE * 3x+2y

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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.