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Given an initial point (x,y), slope function=f(x,y), and a step size h: (Xn+1 Yn+1) Euler's Method (Xn+1 Yn+1) = (xn + h, yn + h* f(xn. Yn)) Improved Euler's Method slope₁ = f(xn. Yn) slope₂ = f(xn+h, yn + h * slope₁) > = (x₂ =xn+h, yn+h* (Xn+1, Yn+1) (slope,+ slopez) 2 Runge-Kutta Method slope₁ = f(xn, Yn) h h slope2 = f (x + 2Y₁+2+ sloper) = (x₂ + 1 = x₂ +h, yn + h * h h slope = f (x + 22. Yn +2 slopez) * slope4 = f(x₂ +h, yn + h * slopez) (slope₁ +2 slope₂ +2 slope3 + slope * 6

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