Hello guys, im new in and I'm having some problems with the differential equations course, could you please help me with some exercises that were left to me in the U. Solving by the homogeneous method

Hola chicos, soy nuevo en y estoy teniendo algunos problemas con el curso de ecuaciones diferenciales, podrían por favor ayudarme con algunos ejercicios que me dejaron en la U.
Resolver por el método homogéneo

Find the arc length parameter along the given curve from the point where tequals=0 by evaluating the integral s(t)equals=integral from 0 to t startabsolutevalue bold v left parenthesis tau right parenthesis endabsolutevalue d tau∫0tv(τ) dτ. then find the length of the indicated portion of the curve r(t)equals=1010cosine tcost iplus+1010sine tsint jplus+88t k, where 0less than or equals≤tless than or equals≤startfraction pi over 3 endfraction π 3.

What are the possible rational zeros of [tex]f(x) = x^4+2x^3-3x^2-4x+18[/tex]

The hawaiian alphabet has 12 letters. how many permutations are posible for each number of letters?