Question

FInd the solution of the first-order PDE:

X^{2} u_{x} + xy u_{y}, u = 1 on x =
y^{2}

Determine where the solution becomes singular?

Answer #1

Find (ux)y and
(uy)x where
x2 + xu - yv2 + uv = 1 and
xu - 2yv = 1

Find the general Solution to the PDE X*Uxy +
Uy = 0 and find a particular solution that satisfies
U(x,0) = x5 + x - 68/x, and U(2,y) = 3y4

Numerical PDE
Find the fourth-order, central difference approximation for
ux.

8. Find the solution of the following PDE:
utt − 9uxx = 0
u(0, t) = u(3π, t) = 0
u(x, 0) = sin(x/3)
ut (x, 0) = 4 sin(x/3) − 6 sin(x)
9. Find the solution of the following PDE:
utt − uxx = 0
u(0, t) = u(1, t) = 0
u(x, 0) = 0
ut(x, 0) = x(1 − x)
10. Find the solution of the following PDE:
(1/2t+1)ut − uxx = 0
u(0,t) = u(π,t) =...

Find the solution of Uy = 2x + y^2 satisfying u(x, x^2 ) = 0

(1 point) Given the following initial value problem
(x2+2y2)dxdy=xy,y(−3)=3
find the following:
(a) The coefficient functions are M(x,y)= and N(x,y)= . (Please
input values for both boxes.)
(b) The separable equation using a substitution of y=ux, is
dx+ du=0 (Separate the variables with x with dx only and u with du
only.) (Please input values for both boxes.)
(c) The implicit solution is
x=
I just need part C.

To write Laplace’s equation, Uxx + Uyy =
0, in polar coordinates, we begin with
Ux = (∂U/∂r)(∂r/∂x) + (∂U/∂θ)(∂θ/∂x)
where r = √(x2+y2), θ = arctan (y/x), x =
r cos θ, y = r sin θ. We get
Ux = (cos θ) Ur – (1/r)(sin θ)
Uθ , Uxx = [∂(Ux)/∂r] (∂r/∂x) +
[∂(Ux)/∂θ](∂θ/∂x)
Carry out this computation, as well as that for Uyy.
Since Uxx and Uyy are both expressed in polar
coordinates, their sum gives Laplace...

Suppose u(t,x) and v(t,x ) is C^2 functions defined on R^2 that
satisfy the first-order system of PDE Ut=Vx,
Vt=Ux,
A.) Show that both U and V are classical solutions to the wave
equations Utt= Uxx.
Which result from multivariable calculus do you need to justify
the conclusion.
B)Given a classical sol. u(t,x) to the wave equation, can you
construct a function v(t,x) such that u(t,x), v(t,x)
form of sol. to the first order system.

Find at least one solution about the singular point x = 0 using
the power series method. Determine the second solution using the
method of reduction of order.
xy′′ + (1−x)y′ − y = 0

Follow the steps below to use the method of reduction of order
to find a second solution y2 given the following
differential equation and y1, which solves the given
homogeneous equation:
xy" + y' = 0; y1 = ln(x)
Step #1: Let y2 = uy1, for u = u(x), and
find y'2 and y"2.
Step #2: Plug y'2 and y"2 into the
differential equation and simplify.
Step #3: Use w = u' to transform your previous answer into a
linear...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 2 minutes ago

asked 2 minutes ago

asked 8 minutes ago

asked 10 minutes ago

asked 10 minutes ago

asked 10 minutes ago

asked 12 minutes ago

asked 15 minutes ago

asked 19 minutes ago

asked 25 minutes ago

asked 27 minutes ago