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

1. Aug 2, 2017

s3a

1. The problem statement, all variables and given/known data
Write the following second-order ODE as a system of two first-order ODEs.

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

2. Relevant equations
w = dy/dt

3. 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?

2. Aug 2, 2017

JosephGirardini

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

3. Aug 2, 2017

s3a

Lol, great. :P

Thanks!