Question

SOLVE USING MAPLE! What would the codes be for solving with maple? I do know how to solve by hand, but a picture of the code inputted in maple is what I’m stuck on. THANK YOU!

Note how this formula for u(r, t) satisfies the wave equation and the boundary condition at z = 0, The other conditions in the wave problem do not concern the points in the region II and thus should not be checked. In the exercises, you are asked to find the values of u in the regions II, III, and IV, by using techniques similar to the ones of Examples 4 and 5. Exercises 3.4 In Exercises 1-8, use d'Alembert's formula (4) to solve the boundary value problem (1) (3) for a string of unit length, subject to the given conditions. In each case, describe completely f and G (an antiderivative of g) (see Ezamples 2 and 3 for hints). 1. f (x) sin Te, g(x) 0, c1 4. f(x) 0, gx)-1,c 1. 5. /(z) as in Exercise 5, Section 3.3, g(x)-x, c 1. 6. f(x)= 0, g(x)= cos π2, c = 1. 7. f(x) 0, g(x)-10, c 1. 8. f(x) 0, g(x) sin πχ, c 1. 0 notormine the first time the string returns to its initial shape in Exercises

Answer 1

The general form of the d'Alembert ODE is given by > dAlembert-ode := y(x)-x4(diff(y(x),x))-g(diff(y(x),x)); dAlembert od (1 where fand g are arbitrary functions. See Differentialgleichungen, by E. Kamke, p. 31. This ODE is actually a generalization of the Clairaut ODE, and is almost always dealt with by looking for a solution in parametric form. For more information, see Examples with(DEtools, odeadvisor) odeadvisor odeadvisor (dAlembert ode) dAlembert The general form of the solution for the d Alembert ODE is returned by dsole in parametric form, together with a possible singular solution, as follows: dsolve(dAlembert ode (4 T- fT)

ee in les, Liven 2. sin (2 (n-t) = f(nt(t) + f(n.at)=dsin(9(nn++) Alaw nor ngonomen