Linear equations of second order with constant coefficients. Find all solutions on displaystyle{left(-infty,+inftyright)}.{y}text{}-{2}{y}'+{5}{y}={0}

Tazmin Horton 2021-02-21 Answered
Linear equations of second order with constant coefficients.
Find all solutions on
(,+).y2y+5y=0
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Expert Answer

gotovub
Answered 2021-02-22 Author has 98 answers

The characteristic equation is given by
r2+2r+5=0
and has the roots r1=1+2i and r2=12i.
The general solution is given by
y=ex(c1cos2x+c2sin2x), where c1 and c2 are arbitracy constant.
This differential equation has infinitely many solutions since there is no initial conditions to determine a particular solution.

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