Question

Solve the PDE 2yu_{x} + (3x^{2} -
1)u_{y} = 0

Answer #1

Hello dear.... I hv solved your problem..... Please upvote... Thank you....

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

FInd the solution of the first-order PDE:
X2 ux + xy uy, u = 1 on x =
y2
Determine where the solution becomes singular?

PDE
Solve using the method of characteristics
Plot the intial conditions and then solve the parial
differential equation
utt = c² uxx, -∞ < x < ∞, t > 0
u(x,0) = { 0 if x < -1 , 1-x² if -1≤ x ≤1, 0 if x > 0
ut(x,0) = 0

1.) 25pt) Solve the IVP: (initial value problem)
y’ = (3x2 + 4x + 2)/(2(y-1)), y(0) = -1

Find the type, transform to normal form, and solve the following
PDE:
uxx - 4uxy + 5uyy = 0

Solve the following non homogenous Cauchy-Euler equations for x
> 0.
a. x2y′′+3xy′−3y=3x2.
b. x2y′′ −2xy′ +3y = 5x2, y(1) = 3,y′(1) =
0.

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) =...

Solve the wave equation Utt - C^2 Uxx = 0 with initial condtions
:
1) u(x,0) = log (1+x^2), Ut(x,0) = 4+x
2) U(x,0) = x^3 , Ut(x,0) =sinx
(PDE)

Solve the non homogenous wave equation , Utt - c^2Uxx =1 ,
u(x,0) = sin (x) , Ut(x,0) = 1+x
(PDE)

The Tricomi equation yuxx+uyy = 0 is a simple and useful PDE
that captures the key characterisitics of transonic flow, where the
supersonic and subsonic flows are present in flow field
simultaneously.
(a) Show that the Tricomi equation is of mixed type. Identify
the regions on the x−y plane where the PDE becomes elliptic,
parabolic, and hyperbolic.
(b) Assuming u(0, y) = u(L, y) = 0, obtain the Airy equation
G′′(y) − k2yG(y) = 0 from the Tricomi equation by...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 8 minutes ago

asked 13 minutes ago

asked 14 minutes ago

asked 17 minutes ago

asked 18 minutes ago

asked 28 minutes ago

asked 36 minutes ago

asked 38 minutes ago

asked 39 minutes ago

asked 54 minutes ago

asked 1 hour ago