Homogeneous linear equations

Calculus Level 1

What is the general solution to the differential equation y ′ ′ + 5 y ′ + 6 y = 0 y''+5y'+6y=0 ?

c 1 e − 2 x + c 2 e − 3 x c_1e^{-2x}+c_2e^{-3x} c 1 e − 2 x + c 2 e 3 x c_1e^{-2x}+c_2e^{3x} c 1 e 2 x + c 2 e 3 x c_1e^{2x}+c_2e^{3x} c 1 e 2 x + c 2 e − 3 x c_1e^{2x}+c_2e^{-3x}

Samir Khan by Samir Khan , 23, USA

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1 solution

Samir Khan
Jun 16, 2016

The characteristic equation is r 2 + 5 r + 6 = 0 ⟹ r = − 2 , − 3 r^2+5r+6=0\implies r=-2,-3 , so the general solution is y = c 1 e − 2 x + c 2 e − 3 x y=c_1e^{-2x}+c_2e^{-3x} .

5 Helpful 0 Interesting 0 Brilliant 0 Confused

yay, very pro solution!

A Former Brilliant Member - 4 years, 10 months ago

describe the constants c 1, and c 2.

David Dyer - 1 year, 7 months ago

they are eigenvectors of the system

David Dyer - 1 year, 7 months ago

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