Please make sure the answer is correct. thank you 1.Consider the ODEWith the initial condition that y=1 when x = 1.LA3.3Numerical Methods for Solving ODERunge-Kutta Methoda. Show that the particular solution is y=- (In x² + x³ + 2).13x-2RK-2b. Use the 2nd, 3rd and 4th Runge-Kutta methods to approximate the value of y at x = 2 using a stepsize of h = 0.1. Complete the table below.RK-3RK Method Step size Approx. value of y Abs. Err. Rel. Abs. Err. (%)RK-42y² + ²y = 3³+y'0.1+10.10.1Show sample of computation below (and attach soft copy of Excel computation).

The given ODE is y'+2xy=3x3+1. The initial condition is y=1 when x=1.

Consider the ODE With the initial condition that y=1 when x = 1. Show that the particular solution is y=(lnx² + x³ +2). b. Use the 2nd, 3rd and 4 Runge-Kutta methods to approximate the value of y at x = 2 using a step size of h = 0.1. Complete the table below. RK Method Step size Approx. value of y Abs. Err. Rel. Abs. Err. (%) RK-2 a. RK-5 RK-4 0.1 0.1 y² + ²y = 23 +1 0.1 Show sample of computation below (and attach soft copy of Excel computation).