1) a) Derive the secant method to solve for the roots of f(x)=0 nonlinear equation, b) Use the secant method to numerically solve the nonlinear equation f(x)= x' – 0.165x² + 3.993 × 104 and assume the initial guesses of the root of f(x)= 0 as x, = 0.02 and x = 0.05 . Condue four iterations to estimate the root of the above equation. Find the absolute relative approximate error at the end of each iteration.

Q: The auxiliary equation of  of  y'''-4y''-4y'+16y=0  is r^(3)-4r^(2)-4r+16=0  . The auxiliary…

A: Given that fr=r3-4r2-4r+16, r∈3,6

Q: What is the general form of a particular solution that should be used when using the method of…

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Q: where y1 = e* is one of the functions in the fundamental solution set. - %3D xy" + (2-2x)y' +(x- 2)y…

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Q: oulli’s equation, x' = a(t)x + f (t)x^n, n /= 0, 1, was proposed for solution by James Bernoulli in…

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Q: 7 0-3 -9 -2 3 18 0-8 y, y(0) = 2 3

A: Given y'=70-3-9-23180-8y Also given y0=23-1   To reduce to row echelon form and solve for constant…

Q: Solve the equation 2 x " y " + 3 x y = (1 + x ) y = ху - which has a regular singula Point x = 0.…

A: Here both p(x)=32xand q(x)=−1+x2x2 aree non analytic at x=0 so 0 is a singular point. But both…

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.