Consider the IVP: x" + (x')² + 6tx = 0, x(0) = 3, x'(0) = 4 Using the Euler method with a time step of At = 0.4 approximate x(0.8) to the nearest thousandth (3 decimal places).

Q: Find the smallest positive root by using Newton- Raphson Method \( f(x)=cos(2x)-x^2 \) with two…

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Q: h(x)=3sinh(1–3x² )cosh(1–3x² )

A: Sinh^-1(x)= ln(x+[√x^2+1]) Cosh^-1(x)=ln(x+[√x^2-1])

Q: Given f'(x) = 5e* + 8x and f(0) = 2 find f. %3D

A: We are given that f'(x)=5ex+8x and f(0)=2. So,

Q: √√3+ rdr then 0 (2)=√√3+230 I X

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Q: Locate the approximate root of cos(x) – xe* = 0 using fixed point method, stop with the iteration if…

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Q: The approximation of the root x' of the function f(x) = x³e* - 1 accurate to within 10-2 using…

A: In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac…

Q: .E(y) = -1.5 E(x) = 15. y = (0.1)x – 3 correct Error

A: Given that, E(y)= -1.5 And E(x)= 15

Q: Suppose the population of a colony of ants grows at the rate P'(t) = 1 +   5 /(√ t + 1)   If…

A: Given, P'(t) = 1 + 5t+1 when t = 120 hours  then P(t) = 250  Thenm  when t = 0 hours then P(t) = ?

Q: In (3x) + ln (x+2y) = A In (4x + y) + ln (5y) = B Find the 5th iteration value of y using the…

A: We have to find the 5th iteration value of y using the successive displacement. Initial value of x…

Q: LET F(X) =2 x SIN(X), AND EPSILON = 2 × 10-7. FIND OPTIMUM STEP VALUE THAT CAN BE USED WITH CENTRAL-…

A: The formula for central difference is  F'x≈Fx+h-Fx-h2h+F'''xh23!+... The optimal value for the step…

Q: = Find k'(x) if k(x) = -5x5/3 Provide your answer below: k'(x) = 1 4 x -1/5

A: Consider the function

Q: thod for the fünction using the given initial guess. (Round you x2 - 5, x1 = 2 f(x.) f(x

A: Given, Using Newton's Method Iteration fx=x2-5,x1=2

Q: Suppose that the net energy generated by a solar panel in a small town up to time t in a day…

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Q: Given the function f(x) = 1/2x4 – x3 – 2,

A: Given function is fx=12x4-x3-2     .....1

Q: min13л1 + 4x1р + 1; — Зл1 + 2т, x'0) = (0.5,0) What is the step size for the first step? use armijo…

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Q: Calculate two iterations of Newton's Method to approximate a zero of the function using the given…

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Q: 2. Show that g(x)= *** has a unique fixed point in [0,1] and find an approximation to the point that…

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Q: Find f. f"(x) = x³ + sinh(x), f(0) = 4, f(2) = 5.6

A: f'' ( x ) = x3 + sinh(x)   , f ( 0) = 4, f ( 2 ) = 5.6    To Find: f ( x )

Q: 2. How much material passes in the time interval [0,1/2] through the points (a) z = 0, (b) z = π/2,…

A: Sol:- To calculate the material passing through a point in the given time interval, we need to…

Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, approximate y'(0.2). (a)…

A: Given y′=2y+3e2x,   y(0)=2,   h=0.1Forth order R-K methodk1=h f(x0,y0) = (0.1) f(0,2) = (0.1)⋅(7) =…

Q: x" + 3x'+2x = t?, x(0) = 1, x'(0) = 2 Solve the IVP and find x(0.25) to at least four decimal places…

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Q: Find the multiple root of f(x) = x'-9x +24x- 20 ith an initial guess of x1 = 0.5 using…

A: According to the given information, it is required to find the multiple roots of the given function…

Q: Use Newton's method to approximate a root of the equation In(5x) = arctan(x -0.1) as follows. Let x₁…

A: X

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.