Let z = 8x2 + 7y2, and suppose that (x, y) changes from (2, -1) to (2.01, -0.98). (a) Compute Az. Az = (b) Compute dz. dz = (c) Compare the values of Az and dz. O dz is a good approximation of Az. O dz is not a good approximation of Az.

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A: Homogeneous LDE with constant coefficient :   A Linear differential equation with constant…

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Q: Show that this function satisfies the initial conditions yp(to) =0 and y'(to) =0, so it is a…

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Q: : Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

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Q: 22) Use Euler method to estimate the solution of the ODE y' (xy?) ,y(1) = 2, h = 0.1 at x = 1.2

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Q: The orthogonal trajectories of y = 9ax is where a is an arbitrary constant y + = 4c 2 Oy +x2 = 9 O…

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Q: Solve numerically y'=x y y(0)=1 for y(0.1)and y(0.2) by modified Euler's method.

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Q: Use Euler method to approximate the value of y(0.1), given y' - 4y = 3x2, y(0) = 5 with Ax = 0.02

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Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy =yx.

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Q: The general solution of 2y" -xy'+ (x - 24 ly = 0, is: OaC,xJ,) + C,xJ_(2) OcC,,(3) + C,xJ_(3x)…

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Q: xy" – 2y' +=y = 7x5 Given that y, = x² and y2 = x are 2 Linearly independent soluti homogenous…

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Q: Given y′ = x2+ y . With y=-1 when x=0. Calculate y(0.4) and y(0.6) using MODIFIED Euler method.

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Q: se Euler method to compute ys for the DE yy'=2 x for y(1)=3

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Q: state where in the ty-plane the hypotheses of Theorem are satisfied 6. y′=ln|ty|1−t2+y2

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Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy = yx.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.