Question

Find the general solution of the given system.

dx/dt=6x-y

dy/dt=5x+4y

Answer 1

Given : dx/dt = 6x-y

dy/dt = 5x+4y

Dividing both the equation:

This is homogenous equation of x and y.

thus, dividing numerator and denominator by "x", gives

let y/x = Y, then y = Yx

differentiating both side

Cross multiplying:

breaking numerator in terms of differentiation of denominator (LHS)

integrating above differential equation:

as integration of f'(x)/f(x)dx is ln(f(x))

and integration of

thus ,

substituting back Y = y/x

ln(x^2)/2 = ln(x), cancelling this term both side,

{C is integral constant}