Differential Equations Answers

Determine the Laplace transform of the function:
f(t)=
{cos(t-(2π/3)) t>2π/3
{ 0 t<2π/3

Form the differential equation having y = (sin–1x)2
+ Acos–1x + B, where A and B
are arbitrary constants, as its general solution

Using method of variation of parameters, solve the equation.
d^2y/dx^2+y=Cosec x

Find the general solution of the differential equation
( 4d"y/dx'')+4(dy/dx)+65y
=65x^2 +8x+73
Show that, whatever the intial conditions,y/x^2--->1 as x reaches infinity

y=x(p²-2p+2)
Please solve for y

Prove that for a two dimensional motion to be possible the stream function and the velocity Potential satisfy the cauchys-Riemanns Equation. Moreover, deduce that both satisfies laplaces equatiin

A tank contains 100 liters of pure water. Brine that contains 0.1 kg of salt per liter enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is the tank after 6 minutes?

Find a power series solution in powers of x . Show the details.

y" + y' + yx^2 =0

The equation of a simple harmonic motion is given as d^2x/dt^2 + ω^2x =0. where the symbols have their usual meaning. The dimension of the quantity ω^2 is
a. L^−1
b. M
c. T^−2
d. LT^−2

d^2x/dt^2+2 dx/dt+2x = 4cost +2sint x(0) =0; x(0)=3