Question

if y'=-xy, y(0)=), then y(0.1) — by Euler's formula​

Answer 1

Answer:

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Step-by-step explanation:

Example :  

 

   Consider below differential equation

           dy/dx = (x + y + xy)

   with initial condition y(0) = 1  

   and step size h = 0.025.

   Find y(0.1).

   

   Solution:

   f(x, y) = (x + y + xy)

   x0 = 0, y0 = 1, h = 0.025

   Now we can calculate y1 using Euler formula

   y1 = y0 + h * f(x0, y0)

   y1 = 1 + 0.025 *(0 + 1 + 0 * 1)

   y1 = 1.025

   y(0.025) = 1.025.

   Similarly we can calculate y(0.050), y(0.075), ....y(0.1).

   y(0.1) = 1.11167