Use Euler's method to obtain a four-decimal approximation of the indicated value. Use h = 0.5 ; y' = 3x^2/2y , y(0) = 1, y(2)

Question.

Use Euler's method to obtain a four-decimal approximation of the indicated value. Use h = 0.5

y' = 3x²/2y , y(0) = 1, y(2)


Solution:

Use Euler's method to obtain a four-decimal approximation of the indicated value. use h = 0.5 y' = 3x^2/2y ; y(0) = 1 ; y = 2

Question.

Use Euler's method to obtain a four-decimal approximation of the indicated value. use h = 0.5

y' = 3x²/2y ; y(0) = 1 ; y = 2

Solution:

Use Euler’s method with h = 0.1 and h = 0.05 to calculate y(1.2) ; dy/dx = 2x – 3y + 1 , y(1) = 5

Question.

Use Euler’s method with h = 0.1 and h = 0.05 to calculate y(1.2)

dy/dx = 2x – 3y + 1 , y(1) = 5

Solution:

Use Euler's Method to compute y(4) given that y' = y - x^2 , y(1)

Question.

Consider the initial value problem y'= y - x², y(1) = 2.

(a) For this IVP, write down Euler's method for y_n+1 in terms of y_n for a general stepsize h.

(b) Using one step of Euler's method approximate y(4).

(c) Using three steps of Euler's method approximate y(4).

Solution:

Use Euler’s method to calculate y(0.5) using h = 0.05 and h = 0.1 y’ = e^(-y) , y(0) =0

Question.

Use Euler’s method to calculate y(0.5) using h = 0.05 and h = 0.1

y’ = e^(-y) , y(0) =0

Solution:

Use Euler’s method with step size 0.5 to compute the approximate y-values y(1.5), y(2), y(2.5) and y(3)

Question.

Use Euler’s method with step size 0.5 to compute the approximate y-values y(1.5), y(2), y(2.5) and y(3)

Solution:

Use Euler's method to obtain a four-decimal approximation of the indicated value. y' = 2x - 3y + 1, y(1) = 3; y(1.2)

Question.

Use Euler's method to obtain a four-decimal approximation of the indicated value. 

y' = 2x - 3y + 1, y(1) = 3;   y(1.2)

Solution:

Euler Method

Use the Euler method with two steps to approximate y(1), where y' = (1 + x)y + x^ 2 , y(0) = 1



Solution