Find the general solution of the given system of odes. { dx/dt =2x 2y,dy/dt =x 3y}

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02-08-2022
Mathematics

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Find the general solution of the given system of odes. { dx/dt =2x 2y,dy/dt =x 3y}

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pragyavermav1 pragyavermav1 · Answer 1 · 2022-08-15T04:43:15-04:00

The general solution of the given system of odes is

m=1 ; m=4 (real roots)

In arithmetic, a system of odes equations is a finite set of differential equations. Any such device may be either linear or non-linear. Also, such a machine can be both a machine of normal differential equations or a system of partial differential equations.

the compatibility conditions of an overdetermined system of odes equations may be succinctly stated in terms of differential forms (i.e., a shape to be specific, it needs to be closed). See integrability situations for differential systems for more.

It is an elaborately based poem praising or glorifying an event or character, describing nature intellectually as well as emotionally. A traditional ode is dependent on three essential parts: the strophe, the antistrophe, and the epode. Distinct forms together with the homostrophic ode and the abnormal ode also enter.

dx/dt = 2x+2y = x^1 = 2x+2y 1

dy/dt = x+3y = y^1 = x+ 3y 2

differentiating 1 with respect to 't'

x^11 = 2x^1+ 2y^1

y^1 = x+3y

x^11 = 2x^1= 2(x+3y)

x^11 = 2x^1+ 2x+ 6y

x^11 = 2x^1+ 2x+ 6(x^1-2x/2)

x^11 = 2x^1+ 2x+ 3x^1- 6x

x^11 = 5x^1 - 4x

x^11 -5x^1 - 4x

x^11 - 5x^1 -4x =0

Auxillary equation is m^5- 5m+4=0

m^2 - m - 4m + 4 = 0

m(m-1) -4 (m-1) =0

(m-1) (m-4) = 0

m=1 ; m=4 (real roots)

Learn more about the system of odes here https://brainly.com/question/15723320

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