1. Find the antiderivative of each of the following functions. 3 a. f(x) =+ e* + Vx b. f(x) = sin (5x) + cos (4x) c. f(x) = 9. - e3x

Q: Consider the following ordinary differential equation y" (x) + y' (x) – 2y(x) = –4x² (a) Show that…

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A: y=Ae5x+Be6x

Q: (i) Integrate the following functions with respect to x: 7 y =- 4x 2x - 3 y = 2 y = x* sin (x° +1)

A: Explanation of the answer is as follows

Q: Determine the general solution of the following FOODE. [1] (x²+1)dy-2xydx=x(x²+1)y*dx (BE)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Given a function : E = 1/2 mv^2 + 1/2 kx^2 Where, x = A cos(wt) v = dx/dt k= mw^2 A, w are constants…

A: Given information: The function is E=12mv2+12kx2, and the value of x=A cos(wt), v=dxdt and k=mw2. To…

Q: 14. The particular integral of the differential d'y _ dy - 2y = e2x for some equation %3! dx…

A: We have to find the particular integral of the differential equation…

Q: 1. Find the differential dy in each of the following. a. y = 2x* – 3x³ – 5x

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Q: Obtain the particular solution for the following set of differential equa dy = (4x2 + 7xy +2y²)dx;…

A: Given that: x2dy=(4x2+7xy+2y2)dx        and when x=2, y=0

Q: I. Evaluate the following function below. 3 2 1. S sin'y ( 2 – 3 cos y )´dy 9 3. S sin'x dx 9 4. J…

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Q: Q1: A. Find of four of the following: dx 1. y = x sin-1 x +v1– x² 2. y = (x2 + 2x) tanh(x + 1) 3. y…

A: See the details solution in below

Q: 1 (a) Evaluate the integration of the following functions: x 2 +2 (i) (ii) fx*e*. dx

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Q: 9. Find the most general antiderivative of the function a) f(x)=12+ sin x b) f(x)= 3x(x-5)

A: see below the answer

Q: dy – 5x-2+ 2x-1 – 6; y(1) =7. dx |

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Q: f) y= xcos(xln x) g) y= 3(sin 2x – x* }** In. 3x'e** h) y= cosx

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Q: 3. Is the expression (ez+y+z +4x²y²2²)dx+(e²+y+z +r’yz²)dy+(e²+y+z+³y²z)dz = 0 %3D exact? If yes,…

A: Given expression is ex+y+z+4x2y2z2dx+ex+y+z+83x3yz2dy+ex+y+z+83x3y2zdz=0 To verify whether the above…

Q: 2. Find the differential dy for each of the following: A. y= x - 2x + 1 +e* B. y=- 2)

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Q: H.W.4 Find dy/dx for the following: 1) y= x+ sin x + sin 5x 2) y 32x + In (sin x) + In(sin 5x) 7) y…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: II. Find the particular antiderivative of the function f(x) = e" (2" – 1) whose graph passes through…

A: Given

Q: find Ly for the given differential operator L and the given function y. Q. L = D2+3, y(x)=ex3(3 is…

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Q: 1. Use the substitution z = following differential equation xy, where z is a function of x, to solve…

A: Properties of integration  ∫1a2+x2dx=1atan-1xa+C∫xndx=xn+1n+1+CddxUV=UdVdx+VdUdx

Q: Find the differential equation of the following function (x – y + 2)dx + 3dy = 0 a. y = x + 5 + Ce…

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Q: - Find a differential operator that annihilates the function f (x) = xe4* – 7x

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

Q: Find a differential operator that annihilates the given function 1. y= 4e* +3e¯* 2. y = 2e cos 3.x…

A: According to our answering guidelines we can only answer 3 subparts at a time, rest you can repost…

Q: 10.verify that each given function is a solution of the differential equation. y′−2ty=1;y=e^t^2…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 25. Let y = e*/10 (a) Find the differential dy. (b) Evaluate dy and Ay if x = 0 and dx = 0.1.

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Q: -cosh(x)dx 18) St?cos(2t)dt S 2y²e»*dy 19) Sxeax+1dx dx Sx²e2*dx 20) S x-x2 ) (2?/ª x)°e-In(x²)e3×dx…

A: We have to find the integration.

Q: Show that the function y =  A e-x    + B x e-x satisfies the differentialequation y"   +2y' + y  =0

A: The given differential equation is y''+2y'+y=0. Let y=Ae-x+Bxe-x. This implies that,…

Q: Which of the following should the function k(x) be in order for the solution of differential k(x) 2…

A: Given that. The solution of the differential equation To find The value of k(x).

Q: -2x + 3x -x) dr- (sin y + y e (y e + +3y e) dy 0. x(0) 1 D 2r-- O 2y - y+ xr e O x+ 2x-y e-3y e+3e–…

A: The given differential equation is,(y2e-2x+3x2-x)dx-(siny+ye-2x+3yey)dy=0, x(0)=1

Q: Q.4 Find the most general antiderivative of the function 1) f(x) = 2x + 1 2) f(x) = cos2x + sin3x…

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Q: T. Selue the ff. differential epnotion ) xy (xdy tydy) = ky'dy; when yol; x=2

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Q: 11) Find the antiderivative: f -3+6√x³ √√x dx

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Q: 1. Suppose that y = x³ + 4x. Suppose we increase x from 3 to 3.02. Use differentials to estimate the…

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Q: Solve the following differential equation y' (x) = y· cos(x) O y (x) = sin(x) + C O y (x) CeCos(z) O…

A: Topic - solutuon of differential equation

Q: 13. Find the differential dy for each of the following. a) y = cos 2x- sin 3x b) y = x2 – V36 – x² |…

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Q: If µ(x) ef (x) is an integrating factor of linear D. E x y' + xf(x) y = x* y – x² sin x where f' (1)…

A: To find - If μx = efx is an integrating factor of linear D.E. x3y' + xfx y = x4y - x2 sinx, where…

Q: 1. Find the general antiderivative. A. S 5x8 4x4 + 10x3 – x² – 9x + 15 dx В. /2 - cos x + sec x ·…

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Q: 7. Determine the following general antiderivatives. cos (x) dx -dx sin(x) а. - b. 10 sin(x)cos(x) dx…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: Solve the following differential equations dy 1 cos x +y = tan x. dx 3. 2y cos x + 4y sin x = sin…

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Q: 1) Find dy for each OF Following functions du a) y = cosh (2n) + 4 ny cosh (1an 2) + 2y = e * %3D F)…

A: Product rule of differentiation:   Chain rule of differentiation:

Q: cos x + x. d'y y=x° + 72x d'y +y-x" 72x because when tho socond deuvative S substituted for dx he…

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Q: Let x and y be differential function of t and suppose they are related by the equatin xy-1=y^2. Find…

A: Differentiating with respect to t, we get

Q: y' + 48y = e 5x sin x 5x differential operator that will annihilate the nonhomogeneity sin x.

A: In the given question, concept of Annihilator method is applied. Annihilator Method The annihilator…

Q: Verify if the given function is a solution of the indicated differential e v = lnsin(x – A) + B:…

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Q: If f(x.v)= e-2x° cos(5x +y),- af dy O a. e-2[4xcos(5x +y) + sin(5x + y)] O b. -e-2x[4xycos(5x + y) +…

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Q: Solve the following differential equation xdy-(y+Inx)dx = 0 Select one: O a. Fx.y) -+iny ++ 1 +-Iny+…

A: We have to solve the differential equation x dy - (y+ln x) dx = 0

Q: use the integrating-factor method

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Q: 6. Given m = pq with a sin p – p = q and b cos q + q = p, find and m a qe. Hint: For calculating…

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Q: 2. Find the following derivatives. (a) y = log; (xe*Y loz Leet (c) y = 38z2-5 (e) h(v) = e-2"…

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Q: e) f1a* +4)*dt

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