How do you find all solutions of the differential equation #dy/dx=y^3sinx#?

1 Answer
Eddie
Jan 1, 2017

# y = pm sqrt ( 1/(2 cos x + C) )#

Explanation:

#dy/dx=y^3sinx#

This is separable

#1/y^3 dy/dx=sinx#

#int \ 1/y^3 dy/dx \ dx=int \ sinx \ dx#

#int \ 1/y^3 dy=int \ sinx \ dx#

# - 1/(2 y^2) = - cos x + C#

# y = pm sqrt ( 1/(2 cos x + C) )#

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