Question

Using the euler method to calculate the following the solution to the problem y′ =x²y²,y(0)=1 numerically for y(0.2) using h=0.1

Answer 1

To numerically solve the differential equation y′ = x²y² using the Euler's method, you can initialize the values, iterate using the method, and calculate the next value of y in each iteration. The final value of y will be the numerical solution for y(0.2).

Step-by-step explanation:

To solve the differential equation y′ = x²y², we can use the Euler's method.

Step 1: Initialize the values. Here, h = 0.1, y(0) = 1, and we need to find y(0.2).

Step 2: Iterate using the Euler's method. Start with x = 0, y = 1, and keep increasing x by h in each iteration until x reaches 0.2.

Step 3: In each iteration, use the equation y = y + h * (x² * y²) to calculate the next value of y.

Step 4: After the iterations, the final value of y will be the numerical solution for y(0.2).