Nonlinear DE Reduction for \ddot{y} = - \dot{y} - y -sin(y)

[sunrah]

Homework Statement

$\ddot{y} = - \dot{y} - y -sin(y)$

Homework Equations

The Attempt at a Solution

to reduce the order I need to find a solution y₁. it seems to me the only obvious solution is y₁ = 0 but i can't use this to do a reduction can i

 

[Infinitum]

Hi sunrah!

You should be able to reduce the given DE to first order by substituting $\frac{dy}{dx}= t$

 

[sunrah]

Hi sunrah!

You should be able to reduce the given DE to first order by substituting $\frac{dy}{dx}= t$

indeed, thank you!

 

[Infinitum]

indeed, thank you!

I hope you didn't write $$\frac{d^2y}{dt^2} = t'$$

 

[sunrah]

i used
$\frac{d^{2}y}{dx^{2}} = \frac{dt}{dx}\frac{dy}{dy} = t\frac{dt}{dy}$

 

[Infinitum]

i used
$\frac{d^{2}y}{dx^{2}} = \frac{dt}{dx}\frac{dy}{dy} = t\frac{dt}{dy}$

Yep, perfect!