Use RK2 (Heun's method) with h = 1/4 to estimate y(4/4) given Yo 30: Y1- Y2: Y3- Y4: 3/13 3/2: Y'3: Y/₁ d²y d02 Find the absolute error relative to the analytic solution y(0) = cos(0). Error in y4: = = −y, y(0 = 0) = 1, y' (0 = 0) = 0.

Q: Find F'(x). SOLUTION IN HANDWRITTEN x 1. F(x) = sin √t dt 2. F(x) = sin t² dt

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Q: Find the general solution of y"+y = cos(t) (a) Using undetermined coefficients (b) Using variation…

A: Find the general solution of (a) Using undetermined coefficients.(b) Using variation of parameters.

Q: CORRECT to find y'(x). d d v'(x) = (In 2z) x (sin u) y'(x) de dx ..... .... .... d y'(x) = sin- dr d…

A: We have to choose the correct answer from the given options according to the given information

Q: particular solution

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Q: Q3) Simplify (if necessary) then Compute: y"+ 2y Where y(x) = (zx+ cosx*)] [4(cosh2x-sinh2x)] d 2,2…

A: To find -  Simplify (if necessary) then Compute : y'' + 2y' where yx = ∂2∂x ∂zz2x + cosx44cosh2x -…

Q: Use the variation of parameter method to find a general solution for the variable coefficient…

A: Given That : differential equation  y"+2tan(x)y'-y=0 ,0<x<1 To find : use the variation of…

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

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Q: dfy = 12 - 30x, y'(0) = 7, and y(0) = 2. dx2 Find the function y(x) satisfying = 12 - 30x, y'(0) =…

A: Given:

Q: Which of these functions (or none of them): (1) z=e" (ycosx-xsiny) or (2) z=e' (y cosx-xsin x) 0²z…

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Q: -1 Find the derivative of the function: y=6 sin ¹¹ (x²). y'= y'= O y'= 12x y'= -X 2x 2 + X 12x 4 4 X…

A: Given y =6 sin-1 (x2 )

Q: cy(1) = 4, y'′(1) = −2. y = x²y" +7xy +9y = xº,

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Q: Let y = sin (x + y), find y'.

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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: Find dy/dx for y = 3l(sin-(e-3**)12 dy 3(sin"(e-*)* In3 2(sin-"(e-3x*)- dx 1(-6х) V1-e-6x2

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Q: (1) Find y' (or 2 if y = 1+2 + V3 + v5x? + 7. (or ) dx

A: Given: y=1+2+3+5x2+7

Q: Find the derivatives for the following functions. 1 2x2 1.

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Q: Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated…

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Q: If y(t) is the general solution for the equation: y' + y = sin(t), y(pi/2) = 0 Then, y(0) = ? a)…

A: Consider the differential equation  y'+y=sint,           yπ2 = 0

Q: Runge-Kutta 4th

A: y' = y-x   , y(0) =2here h = 0.1f(x , y ) = y-xx0=0y0= 2y(0.1) = y(0) +16(k1+2k2+2k3+k4)k1 = (0.1)…

Q: Use the method of variation of parameters to determine a particular solution to the given equation.…

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Q: (d) If x y/1-y², find

A: Solving question1 for other question repost.

Q: f(t) = (cost, Sint, t) f'(t) = (-sint, west, 1) 1 f'(x)) = √√(-sint) ² + ((ost ) ² + 12 F(t)= -…

A: Given that Differentiate with respect to t           Therefore