What is the general solution of the differential equation? : dy/dx=9x^2y
1 Answer
Jun 12, 2017
y = Ae^(3x^3)
Explanation:
We have:
dy/dx=9x^2y
This is a first Order linear Separable Differential Equation, we can collect terms by rearranging the equation as follows
1/ydy/dx=9x^2
And now we can "separate the variables" to get
int \ 1/y \ dy= int \ 9x^2 \ dx
And integrating gives us:
ln|y| = 9x^3/3 + C
:. ln|y| = 3x^3 + C
:. |y| = e^(3x^3 + C)
:. |y| = e^(3x^3)e^C
And as
:. y = Ae^(3x^3)