Home > Calculus > Solving Separable Differential Equations

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

Answer 1

# 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) #

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Cameron Alexander

The general solution of the differential equation ( \frac{dy}{dx} = 9x^2y ) is given by ( y = Ce^{3x^3} ), where ( C ) is an arbitrary constant.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.