Approximate the solution of y'=2x+y, y(0)=1 using Euler's method with | Numerical Methods 0

Numerical Methods05 marksNumerical: Euler's method ODEEuler's method for ODE solving

Approximate the solution of y'=2x+y, y(0)=1 using Euler's method with step size of 0.1. Approximate the value of y(0.4). [5]

Given data: - ODE: $y' = f(x,y) = 2x + y$ - Initial condition: $y(0) = 1$ , so $x0 = 0$ , $y0 = 1$ - Step size: $h = 0.1$ - Target: $y(0.4)$ (requires 4 steps) Euler's formula: $y{n+1} = yn + h \cdot f(xn, yn)$ , with $f(x,y) = 2x + y$ . Step 1: $y(0.1)$ $f(0, 1) = 2(0) + 1 = 1$ $$y1 = 1 + 0.1(1) =...

Given data: - ODE: $y' = f(x,y) = 2x + y$ - Initial condition: $y(0) = 1$, so $x0 = 0$, $y0 = 1$ - Step size: $h = 0.1$ - Target: $y(0.4)$ (requires 4 steps) Euler's formula: $y{n+1} = yn + h \cdot f(xn, yn)$, with $f(x,y) = 2x + y$. Step 1: $y(0.1)$ $$f(0, 1) = 2(0) + 1 = 1$$ $$y1 = 1 + 0.1(1) =...

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