I have done very little on this problem. Sorry if I don't have even begun a solution. The reason is that I am unsure how to do it.
Here's a differential equation: $$ (y'')^3sin(y')+cos(xy')=tan((y')^4) $$
The question is : Which variable substitution would you do to bring this to a differential equation of order 1?
The answer is : p(x) = y'
Considering I'm not supposed to use trigonometric identities, I have difficulty seeing how I can achieve it (but it's ok if you use one... willing to take any solution)
I mean... it would give
$$ (p')^3sin(p) + cos(xp)= tan(p^4) $$
I still don't get it.
How to solve this?