Differential Equations Answers

The demand function and the average cost .Determine the:

Profit function.

Profit. Hence show it is maximum

Find the constants C0, C1, and x1 so that the quadrature formulae z0^1 f(x) dx = C0 f(0) + C1 f(x1),

Has the highest possible degree of precision

Consider the following initial value problems:

y' =e^(x-y) , x is greater than or equal to Zero or x is less than or equal to one , y(0)=0, h=0.5

actual solution: Y (x) = 1/5 x exp (3x) -1/(25) exp (3x) + 1/25 exp (-2x),

a) Use the Euler method to approximate the solutions of initial-value problem, and compare the results to the actual values

b) Use the Heuns Method to approximate the solutions of initial- value problem, and compare the results to the actual values

C) Use the Runge-Kutta method of order four to approximate the solutions of initial- value problem, and compare the results to the actual values

Find the constants c0, c1, and x1 so that the quadrature formulae given by

Roots xi

0.8611363116

0.339981436

-0.339981436

-0.8611363116

Coefficients, ci

0.3478548451

0.6521451549

0.6521451549

0.3478548451

Then use it to find an answer for the following integral

Z1^(1.6) 2x/(x²-4) dx

The indicated function y₁(x)

 is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2,

y₂ = y₁(x) e^{−∫P(x) dx}

y2

1

(x)

dx

        (5)

as instructed, to find a second solution y₂(x).

y'' − 10y' + 25y = 0;    y₁ = e^5x