Question #f058d

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Answer 1 · 2016-11-29T16:36:39

#tan y =x^2/2#

This is a variable separable differential equation

#(dy)/dx=x cos^2 y#

#(dy)/cos^2 y=x* dx#

#sec^2 y" "dy=x* dx#

#int sec^2 y" "dy=int x* dx#

#tan y =x^2/2+C#

using #y=0# when #x=0#

#tan 0 =0^2/2+C#

#C=0#

final answer

#tan y =x^2/2+0#

#tan y =x^2/2#

God bless....I hope the explanation is useful.

Answer 2 · 2016-11-29T16:38:02

The variables can be separated naturally:

#(dy)/(dx)=x cos^2(y) => (dy)/cos^2(y)=xdx#

Integrate both sides:

#int xdx = int (dy)/cos^2(y)#

#x^2/2 + C =tany #

For #x=0, tany|_(y=0) = C => C=0#

#y(x)=arctan(x^2/2)#