Laplace Transform

Use the definition of Laplace transform to find [t*e^kt].

Impulse Forcing

You have a mass-spring system, a unit impulse is applied to this system (at equilibrium,at rest) and the response is recorded and determined to be (10e^-0.1t)- (10e^-0.2t) In general terms what does the form of the impulse response function tell you about the system?

Laplace Transform

if L[f(t)]=F(s) then L[t*f(t)]= -dF/ds use this result to compute L[t*e^kt].

Determine whether the following equations are linear or nonlinear.

a) yy''-y' = sin x b) x^2y''-y'+y = cos x

Show that the operator L defined by

L[y](x)= Integral between 0 and 1 (x-t)^2 y dt is a linear operator. or See attachment...

Determine whether the following functions can be Wronskians on -1

Differential Equation : Find a General Solution

3x^2y'' + 11xy' - 3y = 0, x>0

Solve the Initial Value Problem

y'' + 2y' + y = 0 y(0)=1 y'(0)=-3

Differential Equation

y'''' - 2y''' + 2y'' - 2y' + y = 0

Differential Equation : Wronskian

y'' + p(x)y' + q(x)y = 0 has two solutions x^2 - x and x^3 - x. Use the Wronskian to find p(x).