find the solution of following derivative by Runge-Kutta method f(x,y) = -2x3+ 12x2 - 20x + 8.5 let initial condition at x-0 is y=1 and h=D0.5 = y(0.5) %3D

Q: Given the equation x' = -4yf (x) + sin(y) + 1. Take the derivative for both sides of the equation…

A: Given equation is x3=-4yfx+siny+1 Product rule of differentiation states that: ddxuv=vddxu+uddxv…

Q: 4. y = (8x*- 5x2 + 1)* 5. g(t) = -3V7t3 – 1

A:

Q: 6 Y = x6 + Vx5 ++5 x3 y' = 6x5 +x² – 18x* y' = 6x5 +x1.5 – 18x-2 O Option 2 Option 1 y' = 6x5 +x15 –…

A:

Q: (b) A poll commissioned by a politician estimates thatt days after he makes a statement denegrating…

A: Given: Percentage of constituency that supports a politician is: St=75t2-3t+25t2+3t+25 Derivative of…

Q: = = √²* (t²³ + 5t² + 4) dt 0 If f(x)= then f''(x) =

A:

Q: Use central difference method to estimate the 1st derivative of the following function at x = 2 and…

A:

Q: If ƒ is a differentiable function, find the derivative Y = ƒ(√x) fı x + √√ f(x). 1 ○ y = ƒl (√√x) +…

A:

Q: What is the %ER of the approximate derivative of f(x) = x2ex , using forward-difference %3D approach…

A:

Q: Test the function f (x, y) =x² + y' - 3xy +15 for local maxima and minima and saddle points. Find…

A:

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Find the approximate error, relative approximate error, and absolute relative approximate error of…

A: The approximate error is calculated using the formula: Ea=Present value-Previous value. The relative…

Q: An orchard has an average yield of 36 bushels of apples/tree if the density is 22 trees/acre. For…

A: Let x be the additional number of trees to be planted to maximize the total yield.

Q: A square-based, box-shaped shipping crate with a volume of 16 cubic feet needs to be constructed at…

A: A square based box  Cost of material used for side $p per square feet  Cost of material used for…

Q: The function f is given by f(x)=9.x^2/3+3x-6 has a relative minimum at x=? A. -8 B.-1 C.-1/8 D.0

A:

Q: Use forward, backward, and centered difference approximations to estimate the first derivative of…

A: We are given the function f(x)=5x5+3x3+2x+1 and the step size as h=0.5. As we are given no…

Q: The following quadratic function is given: f(t) = 5t²-7t + 25. i) ii) Use first principle to find…

A:

Q: For f(x) = x2 - 5x + 6, find f(2), f'(2), and f(3) – f(2). a. f(2) = b. f'(2) = c. f(3) – f(2):

A: Given function is f(x)=x2-5x+6 (a) f(2) is obtained by replacing x by 2 in f(x) as follows.…

Q: maximum point of y x – 2

A: Condition for Extreme Value: A continuous function fx, y has extrema at a, b if fx=fy=0 at a, b…

Q: Q1/ find the derivative of the following function 5x? + 2x+3 f(x) =

A: Explanation of the solution is given below...

Q: Find f(x) if f' (x) = 3x – 2x + 3 and f(2) = 15. - f(z) = Preview %D

A:

Q: 15 / 17 116% C. Directions: Solve for the derivative of the following functions using the indicated…

A:

Q: Iff and g are functions that satisfy f(2) = 5 and g'(2) = -3, find h'(2) for h(x) = -4f(x) + 5g(x) -…

A:

Q: What is the approximate value of the first derivative of S(x)=-0.1x*-0. 15x-0.5x-0.25x-1. 2 at…

A:

Q: Use the second forward, backward and central divided difference equations to estimate the second…

A:

Q: 1. f(x) = 4x - 17

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

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.