Solve each equation by the RungeKutta method and fin the val

Solve each equation by the Runge-Kutta method, and fin the value of y at x = 2. Take a step size of 0.1 unit. y\" + y\' ln x + 2.69(x - y)^2 = 6.26y, y\' (1, 3.27) = 8.26

Solution

X\'\' =Dy/dt = f(t,x,v)

X\'= dx/dt = v = g(t,x,v)

Substituting initial conditions

H=0.1

Kf1=f(0,1,0) = 2.69

Kg1= g(0,1,0) = 0

Kf2 = f(0.5,1,3) = 3.57

Kg2 = -3.57

Kf3 = kf4 =3.57

Kg3=kg4 = -3.57

X(1)= x(0) + h/6 (kg1+2kg2+2kg3+kg4)

= 1.006

X\'(1) = 0.994