Question

If y = cos 6x, find yπ​

Answer 1

Answer:

Move the y term to LHS to get cos(t)^2*sin(t)*y’+cos(t)^3*y=1 and recognize that division by cos(t)^2 gives

sin(t)*y’+cos(t)*y=1/cos(t)^2 or (sin(t)*y)’=sec(t)^2 which can be integrated to give

sin(t)*y=integrate(sec(t)^2,t)=tan(t)+k1 so y=(tan(t)+k1)/sin(t) and using y(%pi/4)=0 gives 0=(1+k1)/(sqrt(2)/2) so k1=-1 and the solution is

y=(tan(t)-1)/sin(t)=1/cos(t)-1/sin(t)=sec(t)-csc(t) with plot

Answer 2

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