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 e^x > 0 AA x in RR, we can write the solution as:

:. y = Ae^(3x^3)