# Solving second-order ODE with Runge-Kutta 4

## Homework Statement

Note: I think there is a typo here but I'm not sure. Is there supposed to be a comma between the delta t/2 and y_n on K2 and K3, and delta t and y_n on K4?

See above.

## The Attempt at a Solution

Substituting dy/t = z gives
$\frac{dz}{dt} = 3z - 2ty - cos(t) \frac{dy}{dt} = z$

I'm not sure where to go from here. I can find K_1, but I'm not sure how to find K_2z as it depends on t, y, and z. What do I choose for z in K2? Do I need to redefine K_2 as

$f \left ( t_n + \frac{\Delta t}{2}, y_n + \frac{K_1_y}{2}, z_n + \frac{k_1_z}{2} \right )$ Is there some other way I should approach the problem?

Any help is appreciated, thanks.

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SteamKing
Staff Emeritus
Homework Helper
In K1, there should be a comma between tn and yn.

In K2, K3, and K4, there should be commas between the delta t terms and the yn terms.

Remember z = dy/dt, and you are given dy/dt = 0 at t = 0.

In K1, there should be a comma between tn and yn.

In K2, K3, and K4, there should be commas between the delta t terms and the yn terms.

Remember z = dy/dt, and you are given dy/dt = 0 at t = 0.
This is aimed towards SteamKing, K1 is found with dy/dt=0, but how is K2 solved when f(0.05,1) is undefined by the question and there is no obvious way to determine the f(0.05,1).

Thanks

SteamKing
Staff Emeritus