Ordinary Differential Equation

Find the particular solution of the following differential equation: 12(d^2y/dt^2)-3y=0 given that when t=0, y=3 and dy/dt=0.5 and could you explain the reasons for choosing y=e^(rt)

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.

Solving Linear Homogeneous Differential Equations

Consider the differential equation y’’-2y’+2y = cost (a) Find a general solution to this equation using techniques for solving linear homogeneous differential equations with constant coefficients in combination with a variation of parameters. (b) Use Laplace Transforms to solve this differential equation with the initial c ...continues

Differential Equations : Masses and Springs

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

Differential Equations : Spring with 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

Solving 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.

Systems of Differential Equations : Equilibrium Points and 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.

Derivatives and Rate of Change

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?

Solving 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