How do I solve this second-order differential equation?I want to find θ(t) and I have the following differential equation:d2θdt2=5.36sin⁡θ−0.028(dθdt)2(dθdt)2 is the square of the first derivative of θ(t).

Question: "How do I solve this second-order differential equation?I..."

Adison Palmer

2022-04-15

How do I solve this second-order differential equation?
I want to find

θ (t)

and I have the following differential equation:

\frac{d^{2} θ}{{d t}^{2}} = 5.36 \sin θ - 0.028 {(\frac{d θ}{d t})}^{2}

{(\frac{d θ}{d t})}^{2}

is the square of the first derivative of

θ (t)

srasloavfv

Beginner2022-04-16Added 6 answers

Explanation:
Switch variables and then, write

- \frac{t^{″} (θ)}{t^{'} {(θ)}^{3}} = 5.36 \sin (θ) - \frac{0.028}{t^{'} {(θ)}^{2}}

Now, reduction of order

p (θ) = t^{'} (θ)

is simple.
Do not expect to have

θ (t)

. Keep, if it exists, the implicit solution.

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?