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Differential Equations
Solve the Cauchy problem on a semi-infinite domain:
u_tt - 4u_xx = 0 on 0<x<infinity, t>0
u(x,0) = xe^(-x)
u_t(x,0) = 0
u(0,t) = 0
u_tt - 4u_xx = 0 on 0<x<infinity, t>0
u(x,0) = xe^(-x)
u_t(x,0) = 0
u(0,t) = 0
Differential Equations
Q1 : Differentiate e^2x In(x^2 - 3) with respect to x.
Q2: Differentiate (3x^2 + 2x) e^-x with respect to x.
Q2: Differentiate (3x^2 + 2x) e^-x with respect to x.
Differential Equations
Use D'Alembert's formula to solve the following Cauchy Problem:
u_tt - 9u_xx = 0 on -infinity < x < infinity, t > 0.
u(x,0) = 0.
u_t(x,0) = 2xe^(-x^2)
u_tt - 9u_xx = 0 on -infinity < x < infinity, t > 0.
u(x,0) = 0.
u_t(x,0) = 2xe^(-x^2)
Differential Equations
Consider the pde u_t + (4u^3 + 4u)u_x = 0.
a) Express the pde in conservation form: ∂/∂x[F(u)] = 0.
b) Consider a weak solution in the form of a shock wave: u = {u- if x < λ(t), u+ if x > λ(t)}
Find the speed of propagation λ'(t) of the shock wave.
a) Express the pde in conservation form: ∂/∂x[F(u)] = 0.
b) Consider a weak solution in the form of a shock wave: u = {u- if x < λ(t), u+ if x > λ(t)}
Find the speed of propagation λ'(t) of the shock wave.
Differential Equations
using chain rule find dx/dy of y= u/5+7 and u=5x-35?
Differential Equations
Hi! I have got 35 coordinates (x;y) which seem to form a function of the second degree. I want to know the basic expression for this function, even if I just have the coordinates. These are:
1,3 3,15 4,26 5,37 6,50 7,67 8,74 9,85 10,102 11,125 12,138 13,155 14,174 15,197 16,228 17,257 18,280 19,309 20,352 21,383 22,420 23,463 24,522 25,563 26,610 27,653 28,700 29,761 30,832 31,911 32,970 33,1037 34,1098 35,1181
Thanks in advance!
Gunnar A.
1,3 3,15 4,26 5,37 6,50 7,67 8,74 9,85 10,102 11,125 12,138 13,155 14,174 15,197 16,228 17,257 18,280 19,309 20,352 21,383 22,420 23,463 24,522 25,563 26,610 27,653 28,700 29,761 30,832 31,911 32,970 33,1037 34,1098 35,1181
Thanks in advance!
Gunnar A.
Differential Equations
y’ + y = 2 cos x y (0) = 1
1) Find an approximate solution for y (π/4) by using a power series solution. Use n = 6
2) Find an approximate solution for y (π/4) by using linear interpolation with 10 equal part intervals.
1) Find an approximate solution for y (π/4) by using a power series solution. Use n = 6
2) Find an approximate solution for y (π/4) by using linear interpolation with 10 equal part intervals.
Differential Equations
differential of y=(1+cos^2(3x))^2
I got (1+cos^2(3x))(cos3x)(-sin3x)
but my answer key says (-3cos3xsin3x)/(root of (1+cos^2(3x)))
I got (1+cos^2(3x))(cos3x)(-sin3x)
but my answer key says (-3cos3xsin3x)/(root of (1+cos^2(3x)))
Differential Equations
evalaet the expression or x=6
x2-15
-x-9
x2-15
-x-9
Differential Equations
Solve the Cauchy problem equation:
u_x + u_y = u^2, u(x,0) = 1.
u_x + u_y = u^2, u(x,0) = 1.
