Linear equations of second order with constant coefficients. Find all solutions on {left(-infty,+inftyright)}.{y}text{}+{2}{y}'+{y}={0}

Question

Linear equations of second order with constant coefficients.
Find all solutions on

(- \infty, + \infty) . y + 2 y^{'} + y = 0

Answer 1

The characteristic equation is given by

r^{2} + 2 r + 1 = 0

and has the roots

r_{1} = 11 a n d r_{2} = 1

.
The general solution is given by

y = e^{x} (c_{1} + c_{2} x)

, where c_1 and c_2 are arbitracy constant.

Expert Answer