Question

Find the general solution of the given system. dx dt = 6x − y dy dt = 36x − 6y

Answer 1

Answer:

$y = 6x + C$

Step-by-step explanation:

Given the system of equations

dx/dt = 6x − y  ............. 1

dy/dt = 36x − 6y ............ 2

Divide equation 2 by 1;

$\dfrac{dy/dt}{dx/dt} = \dfrac{36x-6y}{6x-y} \\\\\dfrac{dy/dt}{dx/dt} = \dfrac{6(6x-y)}{6x-y}\\ \\\dfrac{dy/dt}{dx/dt} = 6\\\\\dfrac{dy}{dt}* \dfrac{dt}{dx} = 6\\\dfrac{dy}{dx} = 6$

cross multiply

$dy = 6dx$

integrate both sides of the expression

$\int\limits {dy} = \int\limits {6} \, dx \\\\y = 6x + C$

Hence the general solution to the system of equation is $y = 6x + C$