LaPlace transform

Use Laplace transforms to find the solution of : y'' + 10y' +25y = 180exp(t) with y(0)=1 and y'(0)=1

laplace ODE

Use Laplace transforms to find the solution of : y'' + 2y' = 24sin(2t) + 32cost(2t) with y(0)=1 and y'(0)=0

Differential Equations.

1) consider the equation (non-honogenous): Please see attachment for equation. • find its general solution • find the particular solution of this equation, satisfying the initial condition y(0)=0, y'(0)=0, y''(0)=0 2) find the general solution of the differential equation (non-homogenous) Please see attachment for equation.

Linear Differential Equations

Find the fixed points and sketch trajectories in the phase plane for the system: ... using the phase portrait, examine the behaviour of solutions of this system as t→∞ when they start from (x,y)=(-1,0), and when they start from (x,y)=(-1,-1). Please see attached for full question.

Linear dependency, Wronskian and Bessel's Equation

Three problems regarding the Wronskian and solutions of a second order differential equation. Example of a question 1. Determine whether the following sets of functions are linearly dependant or independent... Please see attached. 2. Bessel's equation x²y" + xy' + (x² - n²)y = 0 where n is a constant, is an important differential equation that arises, for example, in the study of the vibrations of a circular drumhead. a) Let y1(x) and y2(x) be any two solutions to Bessel's equation. Without computing y1 and y2, determine their Wronskian. b) One solution to (1) with n=1/2 is sinx/sqrt(x) Find a second linearly independent solution. c) Compute the Wronskian for ... click for more