Question

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

Answer 1

`y = 6x + C`

Explanation:

Given the system of equations

dx/dt = 6x − y ............. 1

dy/dt = 36x − 6y ............ 2

Divide equation 2 by 1;

`(dy/dt)/(dx/dt) = (36x-6y)/(6x-y) \\\\(dy/dt)/(dx/dt) = (6(6x-y))/(6x-y)\\ \\(dy/dt)/(dx/dt) = 6\\\\(dy)/(dt)* (dt)/(dx) = 6\\(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`