Differential Equations Answers

Solve the Lagrange's equation

(y^2)zp - (x^2)zq = (x^2) y

1, Given Ln(x) - x^2 + 2x = 0 . Solve the equation for the smallest root, using

a) Bisection Method correct up to at least 2 decimal places i.e e = 0.5 x 10^-2

b) False Position Method correct up to at least 2 decimal placesi.e e = 0.5 x 10^-2

c) Compare the two methods according to the number of iterations performed.

2. Construct the convergent fixed point iteration to find the lowest root of the

following equation with an accuracy e = 10^-2.

In(x) — x^2 +7x-8=0

3. Given. e^x +2/3x -2=0

a) Separate the roots using analytical method.

b) Approximate the largest root of the above equation with an accuracy of e < 0.01

using

i) Fixed pointiteration

ii) Newton’s Method

4. Estimate *3 using Secant method with an accuracy e < 0.001

( “^” this sign means power of and “*” this sign means root of )