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 →∞.
using the Laplace transform solve the IVP
y'' +4y= 3sin(t) y(0) =1 , y'(0) = - 1 , i am stuck on the
partial fraction decomposition step. please explain the
decomposition clearly.
5. y′′ + xy′ = 0, x0 = 0 Series Solution Method. solve the given
differential equation by means of a power series about the given
point x0. Find the recurrence relation; also find the first four
terms in each of two linearly independent solutions (unless the
series terminates sooner). If possible, find the general term in
each solution.
1) . Solve the IVP:
y^''+6y^'+5y=0, y(0)=1, y^' (0)=3
2. Find the general solution to each of the following:
a) y^''+2y^'+5y=e^2x
b) y^''+2x/(x^2+1) y'=x
c) y^''+4y=1/(sin(2x)) (use variation of parameters)