# How to convert this ODE to a standard form

1. Jan 9, 2009

### oxxiissiixxo

1. The problem statement, all variables and given/known data

Convert to standard form ODE system y0 = f(t, y):
t^2y'' + sin(y') + 2y − 1 = 0

the goal is to reduce the equation above to be a first order ode.

2. Relevant equations

3. The attempt at a solution

I tried to introduced a new variable but the sin(y') seems tricky.

Last edited: Jan 9, 2009
2. Jan 10, 2009

### chaoseverlasting

What is y0? Also, what is y differentiated with respect to.

3. Jan 10, 2009

### Unco

I'll assume the derivatives are with respect to t. If we let x(t) = y'(t), then the equation becomes (t^2)x' + sin(x) + 2y - 1 =0, which can be solved for x' in terms of t, x, y. In this way we obtain a system of the form [y', x'] = [f(t,x,y), g(t,x,y)].

Last edited: Jan 10, 2009