What is the general solution of the differential equation? : # dy/dx=9x^2y #

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Answer 1 · 2017-06-12T14:57:39

# y = Ae^(3x^3) #

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) #