Write 2nd order ODE as system of two 1st order ODEs

[s3a]

Homework Statement

Write the following second-order ODE as a system of two first-order ODEs.

$d^2y/dt^2 + 5(dy/dt)^2 - 6y + e^{sin(t)} = 0$

Homework Equations

w = dy/dt

The Attempt at a Solution

The solution of the book says $dy/dt = w, dw/dt = -5w - 6y + e^{sin(t)}$, but shouldn't it be $w = dy/dt, dw/dt = -5w^2 + 6y - e^{sin(t)}$, or am I missing something?

 

[JosephGirardini]

I think you are missing the correct solution manual because I came to the same answer that you did ¯\_(ツ)_/¯

 

[s3a]

Lol, great. :P

Thanks!