Use the Nonlinear Shooting method with TOL = 10⁻⁴ to approximate the solution to the following boundary-value problems. The actual solution is given for comparison
to your results. a.yⁿ = y³- yy' , 1 ≤ 2, y(1) = 1/2 , y(2) = 1/3 use h = 0.1; actual solution y(x) = (x + 1)⁻¹ .b.yⁿ =2y³ −6y − 2x³ , 1 x ≤ 2, y(1) = 2, y(2) =5/2 use h = 0.1; actual solution y(x) = x + x⁻¹. c.yⁿ = y' + 2(y − ln x)³ − x⁻¹ , 2 ≤ 3 y(2) = 1/2+ln 2, y(3) = 1/3+ ln 3; use h = 0.1; actual solution d. use h = 0.05; actual solution y(x) = x⁻¹ + ln x d yⁿ =2 (y')² x⁻³ − 9y² x⁻⁵ + 4x, 1 ≤ x ≤ 2, y(1) = 0, y(2) = ln 256; use h = 0.05; actual solution y(x) = x⁻⁵ ln x