What is a solution to the differential equation #dy/dx=(6sinx)/y#?

Question

2400 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-25T13:51:40

# y = pm sqrt( C -12 cosx)#

#dy/dx=(6sinx)/y#

separable!

#y dy/dx=6sinx#

#int \ y dy/dx \ dx=int \ 6sinx \ dx#

#int \ d/dx(1/2 y^2) \ dx=int \ 6sinx \ dx#

#1/2 y^2 = -6 cosx + C#

# y = pm sqrt( C -12 cosx)#