Taylor’s Method of Order

Taylor’s Method of Order
QUESTION 2;
Repeat Exercise 6 using Taylor's method of order four.a. y' = (2 − 2ty)/(t2 + 1) , 0≤ t ≤ 1, y(0) = 1, with h = 0.1b. y' = y2/(1 + t) , 1≤ t ≤ 2, y(1) = −(ln 2)−1, with h = 0.1c. y' = (y2 + y)/t, 1≤ t ≤ 3, y(1) = −2, with h = 0.2d. y' = −ty + 4t/y, 0≤ t ≤ 1, y(0) = 1, with h = 0.1
SOLUTIONS  
Taylor’s method of order four gives the approximations in the following tables.
 
(a)  
 
(b)    
 
(c)  
 
(d)    
QUESTION 3.
Given that; y′′+p(t)y′+q(t)y=0
is 1+t21+t2, and the Wronskian of any of two solutions of the equation is constant.
Therefore; y′′+p(t)y′+q(t)y=1+t
Y1=q+-1, y2=d2, Y2=et+2
Now satisfy that these y1, y2, Y3 in equation……...1
Therefore, we get three equations,
qp + 9(qd-1) =r………a
q + qpt + qr2 =r………b...