How do you find the general solution of the differential equation: #dy/dx=(3x)/y#?

1 Answer
Dec 31, 2016

#y = +-sqrt(3x^2 + C#, (where #C# is arbitrary constant).

Explanation:

We have:

# dy/dx = 3x/y #

This is a First Order separable Differential Equation, so we can just collect terms in #y#, and terms in #x# and "separate the variables" to get:

# int \ y \ dy = int \ 3x \ dx#

We can now integrate to we get:

# \ \1/2y^2 = 3/2x^2 + C'#
# :. y^2 = 3x^2 + C#, (where #C# is arbitrary constant).
# :. y \ \ = +-sqrt(3x^2 + C)#, (where #C# is arbitrary constant).