How to you find the general solution of #yy'=6cos(pix)#?

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Answer 1 · 2017-01-26T01:36:16

#y(x) = +-sqrt(12/pi sin(pix)+C)#

Separate the variables in the equation:

#y (dy)/(dx) = 6cos(pix)#

#y dy = 6cos(pix) dx#

integrate now both sides:

#int y dy = 6 int cos(pix) dx#

#y^2/2 = 6/pi sin(pix) + C#

#y(x) = +-sqrt(12/pi sin(pix)+C)#