Solve Fibonacci Recursion Relation

Solve the recurrence relation x_(n+1) = x_n + x_(n-1), x_0 = 1, x_1 = 1. That it, find a formula for x_n in terms of n

Stability of a 2D recursive relation near a fixed point

Observe that (0,0) is a fixed point of the system: x_(n+1) = u*x_n - y_n + (y_n)^2 y_(n+1) = x_n + (x_n)^4 + y_n Regardless of the choice of parameter u. Determine the range of u values for which this fixed point is stable.

Solve Linear Homogeneous Differential Equations

Not sure how to solve diff. eq. containing first and second derivatives using regular techniques or Laplace Transforms. Please see my example problem attached.

Spring/Weight - Differential Equation

A body that weighs 16 lb. is attached to the end of a spring which is stretched 2 ft. by a force of 100 lb. It is set in motion from a position ½ foot from the equilibrium position of the spring with an initial velocity of -10 ft/sec. (a) Find the differential equation that governs the position of the body over time relative ...continues

Spring problem w/ damping force

A body that weighs 16 lb. is attached to the end of a spring which is stretched 2 ft. by a force of 100 lb. It is set in motion from a position of ½ foot from the equilibrium position of the spring with an initial velocity of -10 ft/sec. Assume the motion of this body is subject to a damping force that provides 6 lb of resistanc ...continues

Differential Equations

Find general solutions to the differential equations (a) y’’+4y = sin2x (b) y’’-2y’+y = x-2ex See attached file for full problem description.

Identifying/describing bifurcation values

Having a little trouble with this particular bifurcation problem. For the one-parameter family dy/dt = y6-2y3+α identify the bifurcation values of α and describe the bifurcations that take place as α increases. See attached file for full problem description.

Equilibrium points/initial conditions

Consider the system: dx/dt = x+2y+1 dy/dt = 3y (a) Derive a general solution (b) Find equilibrium points of the system (c) Find the solution that satisfies the initial condition x(0) = -1, y(0) = 3. See attached file for full problem description.

When did it start to snow?

Early one morning it began to snow at a constant rate. At 7 AM a snowplow set off to clear a road. By 8 AM it had traveled 2 miles but it took two more hours for the snowplow to go another 2 miles. Assuming that the snowplow clears snow from the road at a constant rate (in cubic feet per hour), at what time did it start to snow?

Differential Equations

Find general solutions to each of the following first order differential equations: (a) dy/dt = ty/(1+t2) (b) dy/dt = t + [2y/(1+t)] (c) dy/dt = 2ty2+3t2y2 (d) dy/dt = 3y+3e3t