Question

Find the general solution for the differential equation \displaystyle{\left.{d}{y}\right.}+{9}{x}\ {\left.{d}{x}\right.}={0}dy+9x dx=0 CC, a constant of integration

Answer 1

Answer:

y= CC-4.5x^2

Step-by-step explanation:

To find the general solution to the differential equation

dy + 9x dx = 0, we employ the method of separating variable as follows:

Note: { will represent the integral sign here.

Separating the variables and integrating, we have

{dy  = -{9x dx

y = -(9/2)(x^2) + CC,

where CC is the given constant of integration.

This can be rearranged/simplified to yield

y= CC-4.5x^2