Outcome/s: Max Z = -X1 + X2 + 2X3 ST: X1 +2X2 - X3 s 20 -2X, + 4X2 + 2X, s 60 2X1 +3X2+ X3 s 50 X1. X2, X 20 CO3

Q: Solve the initial value problem. * = et sin (et - 4), y(ln 4) = 0 %3D O A) y = -cos (et - 4) + 1 %3D…

A: Given:-   D.E:dydt=et sm et -4                  Initial condition: y ln 4=0   To calculate:…

Q: 1. f(x) = sin 2x + cos 3x + x² = 0 with xo = -0.5 , Ax 0.1, TOL = 0.001, in [-0.5,1] %3D

A: Given equation is fx=0 where f(x) is defined by fx=sin2x+cos3x+x2  Given initial solution is x0=-0.5…

Q: #35

A: 35) to differentiate the given function

Q: Find the critical numbers of f(0) = 2 cos 0 + sin² 0.

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Q: If x = sec e - cos e and y = sec" 8- cos"0 (x² + 4) (* - n°(y² + 4) = n²(v² + 4) Prove or disprove…

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Q: ∫x+2x√3−6x32x  dx∫x+2x3−6x32x  dx = ∫3sinh(lnx2)  dx∫3sinh⁡(ln⁡x2)  dx =  ∫69+x2  dx∫69+x2  dx =

A: As per bartleby guidelines we only give first three question answers.

Q: Obtain general solution   y¹ = cos²x cos y

A: Obtain general solution  y¹ = cos²x cos y

Q: Increasing and decreasing functions Find the intervals onwhich f is increasing and decreasing.

A: We'll answer the first question only since the exact one wasn't specified. Please submit a new…

Q: 7. Integrate: S sec? (n²x)dx A. 2n tan n² + C В. x sec2 п2 + С C.금tan(T2x) + C D. x sec nx + C 8.…

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Q: Find the general solution of y'=cos²xcosy

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Q: 8. f(x) = 2sin² 3x a. 12cos(3x)sin(3x) b. -12cos(3x)sin(3x) c. 12sin(9x)cos(3x) 9. f(x) = 3 cos² a.…

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Q: From the partial differential equation by eliminating the arbitrary functi on s f and g from = z =f…

A: Given: z=fx+ct+gx-ct

Q: 1. F (x) = sin x+ 2cos x – 5 %3D 2. G(x) = 3e* – 7log;x – 2 * 3. H (x) = 4sec x + 5tanx 4. Z (x) =…

A: Since there are multiple questions. We will solve only the first three questions. If you want to…

Q: dN₁ dt dN₂ dt 5N₁ 1 N₁ 20 N₂ 17 9N₂ 1-- N₂ 20 N₁ 17 1.6- 0.6-

A: This is a question of the equlibrium of the system.

Q: 1. n! n=0 2. (-1)"x2n (2n)! 3. (-1)"x2n+1 2n + 1 n=0 x2n+1 4. E(-1)"- (2n + 1)! n=0 A. sin(x) B. e*…

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Q: 19. Evaluate: S A. VT- x² + arcsin x + C C. – VT- x² + 3arc cos x + C B. – VI- x2 +3 arcsin x + C D.…

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Q: -1-3x+ e3X ) im x>0 hint: L'Hopitals Rule - cos(x)

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Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: esin 2x [In (cos 2a)]? 2esin 2( cos 2x In (cos 2x) + 2 tan 2] 2esin 2a (cos 2x ln (cos 2x) + 2 tan…

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Q: Find a series solution about the ordinary point 0 of the differential equation y" +8xy-4y= 0 O None…

A: To obtain the power series solution of the second order differential equation, use the following…

Q: 5. Obtain the particular solution. y'"-2 y'+2 y=3e" cos 2x; when x 0, y=2,y'=3

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Q: 3. Find the critical numbers of the function f(x) = sin2 3x + cos 3x , 0 <x < 2/3:

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Q: If f(x) = sin(x)e2x, then f"(x) = A) 3sin(x) e2x + 4cos(x) e²*. B) 3sin(x) e2x + 2cos(x) e²x. C)…

A: The given function is: f(x)=sin(x)e2x to find the second derivative f''(x). For that one has to find…

Q: 3. On (-∞, ∞), three functions y₁ (x) = cos 2x, y₂(x) = sin² x, y³(x) = cos² x are linearly…

A: Note: As per the guidelines we are supposed to only one answer because this is not a subparts…

Q: Find the largest t-interval where the solution to the IVP (t − 5)y'' - cos(t)y' + y = 2/t,  y(1) =…

A: Consider the provided question,

Q: Use the method of undetermined coefficients to solve the initial value problem. O y y = y = y = 33…

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Q: The integral of the given function csc x dx is equal to 3cos' x-10sinx cos'x-15sin xcOsx 15sin'x…

A: To evaluate the given integral.

Q: Differential equation in Q3(a) is added with 4e* and 10e* as Y, =6y, + y; +4e* Y, =5y, +2y; +10e"…

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Q: 6. Show that y(x) = Inx is a solution of xy" +y' = 0 on interval (0, 00) but is not a solution on…

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Q: 2 Find the general Solution of yty = 2xcosx -CosX %3D

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Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

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Q: 7.2 (A) 1. S sin x dx cos x + C because(-cos x +C) = %3D dx 2. S cos x dx = because sin x 3. S tan x…

A: We need to solve the given integral. This can be done as follows:

Q: 1261 (2x+1 dz 4-3x -x² 1 (((x+) dx (3) 28 (2x-3 dx √(x²-1) (2x+3) 31 32 33 dx √(x²+1) (2x+1) alx…

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Q: y" - 5y'=x-2, when x = 0, y = 0, y = 2

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Q: Г(x3 + 2х — 1) cos 4x dx A .3 13 x (3x² 13 sin 4x + 4 |cos 4x + C + - 4 32 16 128 B (x³ (3x² 13 |cos…

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Q: Find 2 if x? cos4 cos* T. 1) 2xcos x+4x2cos3xsinx 2) 2xcos x- 4x²cos³xsinx O3) 2xsinx sin xcosx 4)…

A: Hence option (2) is correct.

Q: A Jsin(3x)cos(4x)dx = [ sin(7x) – sin(x). A dx 2 * cos(x) – cos(7x) ® Ssin(3x)sin(4x)dx= [co c) All…

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Q: Compute the general solution valid near the origin ((+4x² )y" - By = O 'y= s{1 - 4x°) + a»\x=…

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Q: 9 Solve: Solve Sut subject to + bux = 0 u(x,0) = +x² зик + 2х их = 0 subject to ✓****/ Rx [0,00) ản…

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Q: 1. L(e** + e¬* + x²) S-4 s+1 s3 e3 2. L(sin 2x + e²x+3) : 2 + s2+4 s-2 Hint: e2x+3 = (e2x)(e³) %3D…

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Q: 17. Evaluate f-3x cos 2x dx a. --cos 2x - 3xsin 2x + C b. -cos 2x -sin 2x + C C. -cos 2x -³x sin 3x…

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Q: 6x² + 5x + 16 S x3 + 3x² + 2x + 6 5 Injx+31+ In (x² + 2)√2 tan ¹() + C Option 1 5 Injx +31+ In (x² +…

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Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y() = 0 O y = cos…

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Q: derrivative of: Cos(xy)+secy=5

A: Consider the given expression as cosxy+secy=5

Q: Solve the initial value DE y - ytanz = sinx, y(o) = 1 5-Cos 2x 5-Cos 3x 5-Cos 2x Cos 2x A) y = B) y…

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Q: sin(x)cos(2x)sin(3x) dx o sin(3x)cos(3x) sin(2x)cos(2x) sin(2x) + C 4 12 8 8 sin(6x) sin(2x)…

A: Solving the problem by finding the integration of the problem.

Q: 5.f(x) = x (x - 1)(*- 2)(* + 1) As x + +o, f(x) = As x - -n, /(x) As x > I co, f(x) – As x > w./(x)…

A: Solution is given below:

Q: (x + 1)³sinx dx x+1)° cosx+3 (x + 1)2 sin x-6 (x + 1)cosx-6 sinx+ C | (x + 1) cos x 3 (x + 1)2 sin x…

A: Solving the problem by finding the integral by oarts method.

Q: 1. y = Arctan 3-V9-x2 2. y = 4 Arccos + 2v4 - x2 2 y = In (*+2), (x-1)2 3. у%3DIn

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Q: n3xcsC3X)ax 3. S sin2xcsc3x+cos²xcsc3x

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…