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
The general solution of equation [tex]\displaystyle{\left.{d}{y}\right.}+{9}{x}\ {\left.{d}{x}\right.}={0}\\[/tex] is [tex]y=-4.5x^{2} +C[/tex].
Given, differential equation is,
[tex]\displaystyle{\left.{d}{y}\right.}+{9}{x}\ {\left.{d}{x}\right.}={0}\\[/tex].
We have to find the solution of this equation.
On separating the variables of the differential equation, we get
[tex]dy= -9x \ dx[/tex]
Now integrating both sides, we get
[tex]\int\ {} \, dy=\int\ {-9x} \, dx +C[/tex] , here C is the constant of integration.
[tex]y=-9\int\ {x} \, dx +C\\y=-9\frac{x^{2} }{2} +C[/tex]
[tex]y=-4.5x^{2} +C[/tex]
Hence the general solution of equation [tex]\displaystyle{\left.{d}{y}\right.}+{9}{x}\ {\left.{d}{x}\right.}={0}\\[/tex] is [tex]y=-4.5x^{2} +C[/tex].
For more details on General solution of differential equation follow the link:
https://brainly.com/question/25731911
