Again considering y'' + 4y' + 3y = 0:
(a) Solve the IVP y'' + 4y' + 3y = 0; y(0) = 1, y'(0) = α where
α > 0.
(b) Determine the coordinates (tm,ym) of the maximum point of
the solution as a function of α.
(c) Determine the behavior of tm and ym as α →∞.
Given the differential equation
y′′-3y′-4y=-2sin(2t), y(0)=-1, y′(0)=1
Apply the Laplace Transform and solve for Y
Y(s)=L{y}
Y(s)=
L(y′)=sY(s)-y(0)and L(y′′)=s2Y(s)-y′(0)-sy(0)
Solve the initial value problem: y'' + 4y' + 4y = 0; y(0) = 1,
y'(0) = 0.
Solve without the Laplace Transform, first, and then with the
Laplace Transform.