Differential Equations Answers

Please solve the following IBVP:

u_tt = u_xx on 0<x<pi, t>0.
u(0,t) = 0, t >= 0.
u(pi,t) = 0, t>= 0.
u(x,0) = sin^3(x) 0<=x<=pi.
u_t(x,0) = sin(2x) 0<=x<=pi.

Find the canonical form of the following PDE:

u_xx - 6u_xy + 9u_yy = xy^2

**Be sure to show the change of coordinates that reduces the PDE to canonical form.

Differentiate
tan((x^2) y-x) = x

form a PDE by elimination f and g from z= f(x2-y)+g(x2+y)

What is 1 inch minus 1/2 inches?

Solve the following Cauchy problem for the nonhomogeneous wave equation.

u_tt - u_xx = 1 on -infinity < x < infinity, t > 0.
u(x,0) = x^2
u_t(x,0) = 1.

Is the function given by u(x,y) = x^2+y^2 a solution of the pde yu_x - xu_y = 0? Why or why not?

Solve the equation (1/x)u_x - (1/y)u_y = 2u on x>0, y>0 with the initial condition u(x,x) = x^2.

water tank is 2m wide and 6m long and holds 36 m3 of water.how deep is the tank

a pharmacist found out at the end of the day she had 5/3 more antidepressions than she had of tranqulizers. She had 32 perscriptions all together. Find out how many tranguilizers there is?

this is an applying equation problem.