Question

Let y ′=−ty+0.1y³ and y(0)=0.89. Use Euler's method to find approximate values of the solution of the given initial value problem at t=0.5,1,1.5,2,2.5, and 3 with h=0.05

Answer 1

To use Euler's method, start with the initial condition and the differential equation, then use the formula to approximate y at different time points.

Step-by-step explanation:

To solve this problem using Euler's method, we need to start with the given initial condition y(0) = 0.89 and the differential equation y' = -ty + 0.1y^3. We can use the formula y(i+1) = y(i) + h * y'(i) to approximate the values of y at different time points.

Using h = 0.05, we can calculate:

At t = 0.5: y(0.5) = y(0) + h * y'(0) = 0.89 + 0.05 * (-0 * 0.89 + 0.1 * 0.89^3)

Similarly, we can calculate y at t = 1, 1.5, 2, 2.5, and 3 by substituting the previously calculated values of y into the formula and evaluating y' at each time point.