4. ((cos 4t)i + (sin 4t)j + (6t)k) dt - 4

Q: Q2- (75 %): Classify and Solve; d?y dy cos? t + cosht + sinh t + sin? t +3 sin t - 3t + 9 %3D dt2 dt

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Q: 7.Obtain the general solution using the method of undetermined coefficients. a. (D² + D)y = - cos x…

A: First we put auxiliary equation D2+D=0 then solve it.

Q: 5. Find the general solutions of the equations i) Zx - 4z,, – 5z, +10z, = cos(x+3y)-sin(x+3y) %3D

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

Q: 2) find the radius and coordinate center for the equation 2x42y+10y-12х-20-0 3) prove that sin 2x…

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Q: -3+ Sin zt dt 7 8-1 i uct-1) } e-zt 9- to

A: As per our guidelines I am solving only 1st for others kindly resubmit the question mentioning that…

Q: Solve the given DE x?dy - xydx-2ydx

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Q: 2. Solve for y in terms of x for the following equations: a) In(1- 2y) = x %3D b) In(y- 1) - In 2 =…

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Q: (3х' - 4х- 3) x* – x' +x² – -* dy = cos ydx – - 1- sin? y y

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Q: Please solve using 2nd Order and 4th Order Runga-Kutta y'=ysin^3(t)       y(0)=1 t= 0 to 3   h=0.1

A: Since, we have maximum pages uploaded is 10. So We give you only solution of second order RK method.…

Q: Topic: Variable Separable and Homogenouse D.E. I need particular solution for 4

A: We have to solve

Q: 2. Solve by: a) Fixed point, b) Newton-Raphson, and c) Secant methods: xex – 2 = 0 For a) and b),…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: (10) The result of (D-3D D, +2D;)sin(x-2y) is

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Q: 41. Let a, b, r bc constants. Show that k sin rt - r cos rt y = Ce-kt +a + bk k2 + r2 is a general…

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Q: 4+t -1 -1 3 y + t· sin "(2t) - 5[tan (6t)]° + cosh(t) + 4ln t. 3t te dy Find:- -.Don't simplify your…

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Q: 7) Suppose a is a positive constant less than 7. Prove that the equation 2r+cos r = a has a real…

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Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* – 4e* = Asinhx+B coshx

A: Definition used: sinhx=ex-e-x2coshx=ex+e-x2 Consider the given equation as 5ex-4e-x=Asinhx+Bcoshx…

Q: 24 dx J1- cos (8x) 24 dx J 1- cos (8x)

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Q: 5. Let y (sin(2r)) (nz). Find 2. Express your answer only in terms of r.

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Q: 2. Solve by: b) Newton-Raphson, and c) Secant methods: xex – 2 = 0 For a) and b), let xo = 1; for c)…

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Q: 1. how that { cos(Inx), sin(Inx)} is a fundamental solutions set for x²y" + xy' + y = 0 on the…

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Q: 1) x² sin(y') + xe2 – cos(z?) = 3y– 6z + 8 cos(z?) = 3y – 6z + 8 %3D -

A: Given; x2siny3+xe3z-cosz2=3y-6z+8 Now differentiate partially with respect to x we get,…

Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, + 3i.…

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Q: 6. y = C, cos x + C2 sin x + C3 cos 3x + C4 sin 4x ; C1, C2, C3 and C4 are arbitrary constants

A: The given equation is, y=C1 cos x+C2 sin x+ C3cos 3x+C4sin 4x Differentiate this equation up to the…

Q: 1.14 To determine L sinh(3t)cos (t) , f(t) = sinh(3t)cos? (t) must be rewritten as %3D - e sinh( 3t)…

A: Laplace Transform Definition: Given a function ft defined for all real t≥0, the Laplace transform of…

Q: (4r + 5)2 2 dr + tan r-y = Cos z

A: Given differential equation is 2dydx+tan x·y=(4x+5)2cos xy3

Q: Q\ use Euler's method to the differen fial equa tion Solve y=XVXY When y co) =\ cnd

A: For the solution follow the next step.

Q: 5. 2 sin7 0 cos Od0 )dy 1 6. JF(ylny 9-y².

A: Use the method of substitution to solve a given problem.

Q: The Existence and Uniqueness Theorem guarantees that the solution to (t+ 2)y"-sint y+ e2t у-1) - о…

A: Given differential equation is :  (t+2) y'' - sint y' + tt-4y = e2tt ,  y(-1) = 0

Q: у 3 Сі сos 2х + с2 sin 2x y = cqe2* + c2xe²2x

A: See the details solution in below

Q: (Q6) Solve the following non-linear algebraic equations: (a) 2ex + sin 2y + 22 5, sinhx + 22+1 2sin…

A: Since you have asked multiple questions, we will solve first question for you. For other question,…

Q: 6. f(t)=-e" sin (2r + 7) -2t 7. f(1)= 3e " cosh (In 21) %3D

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Q: 2. Obtain the general solution of the ODE (2a² – r²) dr = r³ sin 0 d0.

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Q: 5. Use Newton's method to find the root, xx, of the equation, f(x) = x² e-- 0.6, up to machine…

A: Given: 5. f(x)=x2e-x-0.6 To find: Root of a given function using Newton's method starting with…

Q: 1) When using the Newton-Raphson method to solve the equation cos(ax) = x,this is done one of the…

A: The given equation cos(ax)=x Newton-Raphson method algorithm: The method is used to find the…

Q: 1. Solve the hyperbolic function of the following. i. cosh (-2 + j3) in the form of a + jb ii. sinh…

A: some formula  coshx+jy=coshxcosy+jsinhxsinysinhx+jy=sinhxcosy+jcoshxsiny i.…

Q: # 2. So sin 32 dz C: Izl=3 (z-5)

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Q: 3 Г 3 +x = 2. - -xT secIX 4 .a O T COsecTX bO 4 +> T COseCTX .c O - +x2 4 T secTX .d O -

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Q: What is r = -12 2 cos 0-7 sin e 2y - 7x = -12 in Cartesian form? x² + y² = -12 2x-7y

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Q: 10. If h(x) = x²2cos 2x, then h'(1) = A. 4cos 2 B. 2· 2cos 2x (1 + In 2) C. 21+cos 2 D. 21+cos 2 (1…

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Q: 3. Given that 2 = 6²¹ sin (u + ), e2v Use chain rule to find az/0x when x = 0, y = 0. u=e¹ - sin (y…

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Q: The differential operator D2- 8D+80 has the form D2- 2aD +a² + B? where a = and B= Therefore D - 8D…

A: Consider the given differential equation: D2-8D+80            f=e4xcos(8x) and g=e4x sin 8x which…

Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* - 4e* Asinh x+B coshx…

A: Consider the following equation:…

Q: 2. [ (1–3x)sin(}x)dx 4w dw 3. [* w°e™ dw w²e* -1

A: This question is taken from the definite integral in which we have to find the integral of the given…

Q: 2. Solve the IVP y(3) + y" = 5 cos(2.x), y(0) = 3, y'(7) = 1, y"(0) = 0

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Q: 35. In the integral x €, 1), which values of x satisfy the -3n 2 equation cos x 2 а. 1 b. 2 с. 3 36.…

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Q: 2 Show that y = sin(t) is a solution to ( dt =1– y. To do so, compute each side of the equation in…

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Q: ¹{.(²-1)} = Q4. C-1 (a) cosht - 1 (b) (c) 1 2 (d) 1 - cosh t [cos 2t - 1] [sin 2t - 1]

A: Here, to find the inverse Laplace transform of the function: 1s(s2-1)=1s(s-1)(s+1) Now, using…

Q: 44. First verify by substitution that y (x) =x=1/2 cosx is one solution (for x > 0) of Bessel's…

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Q: 4e + 6x° + 9 cos z)dr %3D

A: Given

Q: Enei Jan-19snk[(2n – 1)8] = %3D Select one: CO a. súnh(sink8) 4 Obsink(sink8) 4 3. o d. sinh(4sink8)

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