Verify by direct substitution that the wave function for a standing wave given in the equation below is a solution of the general linear wave equation, shown below. (Show all work)
Verify by direct substitution that the wave function for a standing wave given in the equation...
Verify by substitution that the given function is a solution of the given differential equation. Note that any primes denote derivatives with respect to x. y' = 4x3y = x + 6 What step should you take to verify that the function is a solution to the given differential equation? O O O O A. Substitute the given function into the differential equation, B . Integrate the function and substitute into the differential equation C . Determine the first and...
PrOBleM: SoLuTiONS To THE WAvE EQuATION a) By direct substitution determine which of the following functions satisfy the wave equation 1. g(z, t)-A cos(kr - wt) where A, k, w are positive constants 2. h(z,t)-Ae-(kz-wt)2 where A, k, ω are positive constants 3. p(x, t) A sinh(kx-wt) where A, k,w are positive constants 4. q(z, t) - Ae(atut) where A,a, w are positive constants 5. An arbitrary function: f(x, t) - f(kx -wt) where k and w are positive constants....
By direct substitution, demonstrate that the following wave function for the infinite well, 2 . no is a solution of the Schrödinger equation in the case of E- 2ma2
a) By direct substitution determine which of the following functions satisfy the wave equation. 1. g(x, t) = Acos(kx − t) where A, k, are positive constants. 2. h(x, t) = Ae where A, k, are positive constants. 3. p(x, t) = Asinh(kx − t) where A, k, are positive constants. 4. q(x, t) = Ae where A, a, are positive constants. 5. An arbitrary function: f(x, t) = f(kx−t) where k and are positive constants. (Hint: Be careful with...
Verify that the given function is a solution to the given
differential equation (c1 and c2 are arbitrary constants) and state
the maximum interval over which the solution is valid.
For Problems 7-21, verify that the given function is a solu- tion to the given differential equation (cy and c2 are arbitrary constants), and state the maximum interval over which the solution is valid. ya Sx +42 25 WID#cigos x A Asin 2%, = 0 BAWK vel Hope 2y +10....
correct me if wrong
Verify by substitution that y is the solution for the differential equation Y' + 4y = 1.4 The solution is y = Cel-4x) + 0.35 Where the initial Condition (IC) is given by: y(x=0) = 2 y = dy +4y=114 Cdx) dx dy +4y= 1.46dx) dy +4(2)=11444 dy +8=1,4dx
Verify that the given function is a solution to the given
differential equation (c1 and c2 are arbitrary constants), and
state the maximum interval over which the solution is valid.
14. y(x) = cix-3 + c2x-1, x2y" + 5xy' + 3y = 0.
verify that the given function is a solution to the given
differential equation (c1 andc2 arbitrary constants), and state the
maximum interval over which the solution is valid.
8. y(x) = cj cos 2x + c2 sin 2x, y + 4y = 0.
a-v- 102t , . consider- 29, The linear wave equation is given by the left hand side of the linear wave equation. Must show work for credit. v vot2. Consider ψ= Acos(kz we). 2 that is part of the linear wave equation. Must show work for credit. 30. The linear wave equation is given by = Calculate 31. The linear wave equation iiven by ar-la ait う. Consider v = Acos(kz-ut). Now that you calculated the partial derivatives show that...
Verify that the indicated function is an explicit solution of the given differential equation. Give an interval of definition I for the solution. y" + y = sec(x); y = x sin(x) + (cos(x)) In(cos(x)) O [0,7) O (-0,0) O (-0,-) O (0 ) O(