Differential Equations Answers

dx/dt=x-4y

dy/dt=x+y

A 16 lb weight is suspended from a spring having spring constant 5 lbft. Assume that an external force given by 24 sin (10t) and a damping force with damping constant 4, are acting on the spring Initially the weight is at rest at its equilibrium position. Find the position of the weight at any time. Find the steady state solution. Find the amplitude, period and frequency of the steady state solution. Determine the velocity of the weight at any time

((D-3D'-2)^3)z=6(e^2x)sin(3x+y)

Solve:

• dy/dx - 2y = 5y²

Suppose a population of insects according to the law of exponential growth/decay. There were 130 insects after the third day of the experiment and 380 insects after the 7th day. Approximately how many insects were in the original population?

Solve the ODE by Linear ODE method:

x dy/dx + 3y = 6x

Determine whether each of the equations is exact. If it is exact, find the solution.

1. (dy/dx)=-(ax-by/bx-cy)
2. (2x+4y)+(2x-2y)y'=0
3. (3x²-2xy+2)+(6y²-x²+3)y'=0
4. (ycosx+2xe^y)+(sinx+x²e^y-1)y'=0

Determine the order of the given differential equation; also state whether the equation is linear or nonlinear.

1. t²(d²y/dt²)+t(dy/dt)+2y=sint
2. (1+y²)(d²y/dt²)+t(dy/dt)+y=e^t