Solve the question 3 by python

1. python (1) Composite Simpson's Rule():y,ex dx,n=100 (2) Runge-Kuta Method of order 4:t, to yo, hun,tw; printz w, y' = y(2-y), 0(0) = 0.1, A= 0.2, I = 5 5 steps) 2. ),, Romberg Integration Composite Trapezoidal Rule f(x)dx( , | 10.0 0.5 f(x) 1.0000E+00 18.8250E-01 16.0653E-01 3.2465E-01 1.3534E-01 4.3937E-02 1.1109 E-02 2.1875E-03 3.3546E-04 | 2.0 2.5 3.0 3.5 4.0 | | | | 3. a Implicit Trapezoidal Method Wj+1 = w; + f(t),w;) + f(tj+1,Wj+1)] *** y = f(ty) = -15y, y(0) = 1 -h=1/8.1 = 818 steps)) Wi+1, | chara) -- + y + (cono) = -15wan with by + f(xy) = 0 1 + = " + (row)(S-15 +1) 1. python (1) Composite Simpson's Rule():y,ex dx,n=100 (2) Runge-Kuta Method of order 4:t, to yo, hun,tw; printz w, y' = y(2-y), 0(0) = 0.1, A= 0.2, I = 5 5 steps) 2. ),, Romberg Integration Composite Trapezoidal Rule f(x)dx( , | 10.0 0.5 f(x) 1.0000E+00 18.8250E-01 16.0653E-01 3.2465E-01 1.3534E-01 4.3937E-02 1.1109 E-02 2.1875E-03 3.3546E-04 | 2.0 2.5 3.0 3.5 4.0 | | | | 3. a Implicit Trapezoidal Method Wj+1 = w; + f(t),w;) + f(tj+1,Wj+1)] *** y = f(ty) = -15y, y(0) = 1 -h=1/8.1 = 818 steps)) Wi+1, | chara) -- + y + (cono) = -15wan with by + f(xy) = 0 1 + = " + (row)(S-15 +1)