Solve Ut 2ux + 9u = 0, -x< x < ∞, t> 0 u(x, 0) = 7 cos(x) First change to characteristic coordinates (§, s) where s = t and ξ = help (formulas) picked so that when s Us + - = t = 0 then § = x, and that the equation becomes an ODE in s : 0 help (formulas) Now write u in terms of (ε, s): u = ☐ help (formulas) Finally write u in terms of (x, t) : u = help (formulas) Book: Section 1.9 of Notes on Diffy Qs

Find the following derivatives:

Find the derivative

Find dr/dtheta for theta^(-7/9) + r^(-7/9) = -5

Use inverse functions where needed to find all solutions of the equation in the interval [0,27). cscx - 7cscx = 0 arcsin +2 n, arcsin O arcin-) arcsin + T, arcsin arcsin + T, arcsin +2 7 arcsin +T, arcsin

Use implicit differentiation to solve the following questions.  x^2-2xy+5y^2=6

By using equation qx= 2mx/(2+mx) , derive a similar equation for the more general case of an age group of width years (x to x+n years) that is show tha nqx = (2*n* nmx) /(2+n*nmx)

please help me to find the derivative of this question and please explain the each steps you do

explain each one please

For each of the following, find y^1 You do not need to simplify your answer. PLEASE attach an image so that I can understand each and every step.