Differential Equations Answers

look at the partial differential equation
xux - tut= u

show that u( x , t) = xf( xt) is a general solution , where f is any differentiable function

solve the wave equation c^2 uxx = u tt for t ≥ 0 0 ≤ x ≤ π . Take c = 1 , take initial and boundary conditions

u(x , 0) = sin x and ut(x , 0) = 0


u( 0 , t) = u ( L , t ) =0 ?

use the laplace transform to solve the follwing initial value problem

y''-y'-6y=-6t+11 , y(0)=-1 y'(0)=4

show that given equation is homogeneous and solve
(x^2+xy)dy=(x^2+y^2)dx

I am looking for assistance in starting to solve this problem. Dont need the answer but a methodology for figuring it out on my own. A particle moves from right to left along the parabolic curve y = square root of -x in such a way that its x coordinates decreases at the rate of 4 meters per second. How fast is the angle of inclination in degrees of the line joining the particle to the origin changing when x = -2?

find the laplace transform of
1) f(t)=(1+te^-t)^3

what is the derivative quotient of 6x-5/2x-1

.1. If L(f(t)) = F(s), then show that L(f(at)) = ( )
2.Write a function for which Laplace transformation doesnot exist. Explain why
Laplace transform does not exist.
3.Find the Laplace transform of
t
1
.

Solve these equations
dx/dt = (i w1 /2) exp (-i(w0-w)t)
dy/dt = (i w1 /2) exp (i(w0-w)t)

initial conditions are x=1,y=0 at t=0

(890 - 429) x (754 x 468 + 670) = ?