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## 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?

## Homework Equations

See above.

## The Attempt at a Solution

Substituting dy/t = z gives

[itex]\frac{dz}{dt} = 3z - 2ty - cos(t)

\frac{dy}{dt} = z[/itex]

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

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

Any help is appreciated, thanks.