Consider the following IVP: x" + 4x = t+4; x(0) = 1, x'(0) = 0 Find the general solution. 1 1 (A) x(t) =-t--cos2t+2 8 8 1 1 B) x(t) =-t--sint-1 8 4 (C) x (t) sinh – sinht+2 4 8 1 D x(t) =-t--sin2t+1 4 8

Q: Determine the value of k such that k y=(1-sinx) * is a solution to 2y'=y³cosx

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Q: = 1- Solve y"+6y' +9y=2xe * + 3 + 2x²

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

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Q: Find the general solution of (D²-7DD' + 12D'2)Z = sin(x - 2y) + ex-2y

A: This question is from linear partial differential equation.

Q: (xii) f(t) = 3e'cosh4t (xiii) f(t) = 3e-2"(sinh2t – 2cosh2t)

A: Given :-  The table of Laplace transforms below and any relevant properties used. (xii) f t = 3 et…

Q: 5. (3x-17) dx / (x² - 6x + 10) 11

A: As per our guide lines we are supposed to answer only one question. Kindly repost other questions as…

Q: (a) x = t* - t + 1, y = t2 Select--- v (b) x = 2 - 2t, y = VE --Select--- v (c) x = sin(2t), y =…

A: Match the graph with their parametric equations.

Q: Q1: Find dy/dx for the following functions (solve four only):-

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Q: The general solution of dy/dx-2/x y=(y/x)^3 sin [x] is y^(-2)=1/x^4 (2x cos [x-2 sin [x+c)] O A.…

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Q: Show, by drawing, that the following graphs are planar: the wheel W5;

A: The graph of W5 is in next step

Q: Find f. f"(x) = 5 + cos(x), f(0) = -1, f(9π/2) = 0

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Q: Use var of par to find a particular solution yp of ( 1² - ²1 ) y = t t₂ t² (y") + t (y') + t²

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Q: Find y = 223 [tan(3r+1)] 2° + ry – y5 = 8x2 = (x + 3)² (x² – 2x) -

A: The Product Rule : The Product Rule says that the derivative of a product of two functions is the…

Q: The solution to the IVP, is x₁ = 13x1 x2, x1(0) = x2 = 34x1+7x2, x2(0) = -1 x1(t) = e10t (cos(5t) +3…

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Q: 9x²– e 2x Given by a function of x is equal to v1 – cos²x + 0. find the roots of equation with…

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Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: Which of the following is a solution to x' A(f) x +b (t) if -2 1 A (1) = -3 2 b(t)= 2 sin(t) -…

A: To find -

Q: f"(x) = f(x) = (x + 6)(x − 6)(x +,5)(x – 5) X Solve the equation f'(x) = 0. (Enter your answers as a…

A: To find second derivative of

Q: Q7// find the general solution (sin-1x + 1 y)dx + sec-1xdy = 0 1 xVx² – |

A: The detailed solution is as follows below:

Q: Find the general solution: 2y" + 3y' +y = 2e2 + x² + 3 sin(x).

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Q: Solve using the method of undetermined coefficients: y" + 8y' = 2x¹ + x²e-³x + sin (x)

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Q: Find f. f"(8) = sin(0) + cos(8), F(0) = 5, f(0) = 4 F(8) -sin(0) – cos(0) + 5x + 6

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Q: Find (f 1)' (a) f(x)=3x³+4x²+6×+5₁ a=5 f(x) = x³ +3 sinx + 2 cosx, q=2 f(x) = 3+x² + ton (₂),…

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Q: Use the method of undetermined co – efficient to solve: y'' + 2y = sin (x)

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Q: The velocity of a particle moving back and forth on a number line is ds = 3 sin(3t) dt for all…

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