Differential Equations : LaPlace Tranform Method

Use the LaPlace transform method to solve the initial-value problem y'''+y''-2y'+y=cos2t, y(0)=1, y'(0)=0, y''(0)=-1 Please show all work! Thanks

Find General Solutions to a 2nd and 4th Order ODE

a) y'''' - 11y''' +45y"-81y'+54y = (t+1)e^(3t) b) y''+y=tcost

3rd order DE using Variation of Parameters

y"'+4y' = cot 2t variation of parameters to solve above equation.

Use the elimination method for systems with constant coefficients to solve the following system of equations.

(D-3)[x] + (D-1)[y] = t (D+1)[x] + (D+4)[y] =1

Ordinary Differential Equations and Initial-Value Problems : Unique Solution

Find the unique solution satisfying initial conditions y(1)=0 and y'(1)=1 for ty''-(t+2)y'=2y=0, t not equal to 0 Solve t^2y''+3ty'+5y=0 Solve the initial value problem. y''-2y'+y=2e^t+3 y(0)=4 and y'(0)=3

Second Order

Find general solution of a second order differential equation.

Problem involving diff eq'ns

A mass 5kg is attached to a spring suspended from the ceiling. When the mass comes to rest at equilibrium, the spring has been stretched 2m. The mass... Determine the motion of the mass. Decribe its motion in as much detail as possible. Please see attached.

Initial Value Problem

Solve the initial value problem... Please see attached.

Differential equations

I am looking for the best statements about solutions and how is the statement supported... Please see attached.

Second order Diferential equation with Wronskian

Let y1, y2 be twice differentiable functions on an interval (a,b) whose Wronskian is nowhere zero. Show that there... Please see attached.