Question

solve the classical wave equation using Heun's method.

Answer #1

solution

4 Schr¨odinger Equation and Classical Wave Equation
Show that the wave function Ψ(x, t) = Ae^(i(kx−ωt)) satisfies
both the time-dependent Schr¨odinger equation and the classical
wave equation. One of these cases corresponds to massive particles,
such as an electron, and one corresponds to massless particles,
such as a photon. Which is which? How do you know?

Solve the following differential equation using the method of
Laplace Transforms. ? ′′ + 2?′ + ? = 3,
?(0) = 0,
? ′ (0) = 0.

Solve the following wave equation using Fourier Series
a2uxx = utt, 0 < x < pi,
t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sin2x - sin3x,
ut(x,0) = 0

Solve the following equation by using the frobenius method
y ′′ + xy′ + (1 − 2 * x ^ (-2) )y = 0
No point is given.

Solve the following wave equation using Fourier Series
a2uxx = utt, 0 < x < pi,
t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sinxcosx,
ut(x,0) = x(pi - x)

Solve the following wave equation using Fourier Series
a2uxx = utt, 0 < x < L, t
> 0, u(0,t) = 0 = u(L,t), u(x,0) = x(L - x)2,
ut(x,0) = 0

Solve differential equation by using variation of parameter
method
y^''+y= cosx/sinx

Solve the following partial differential equation using
separation of variables method
[Marks 10]
?2?/??2− ???/?? +??/?? = ?.

differential equations!
find the Differential Equation General Solve by using
variation of parameters method...
y''' - 3y'' +3y' - y =12e^x

how
would you solve the below diophantine equation using thw method of
congruence. - number theory
Show that the equation 11x^2 + 10x - y^2 + 2 = 0 has no
solutions.

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