13..2/√29 (just use the formula)
5. The solution of the differential equation cos2 xdy/dx+y = tan x is
(a) y = tanx + ce–tan x
(b) y = (tanx + 1) + cetanx
(c) y = (tanx – 1) + cetanx
(d) y = (tanx – 1) + ce–tanx
6. The solution of the differential equation dy/dx + 2ytan x = sin x, y=0 at x= π/3 is
(a) y = cosx – 2 cos2x (b) y = cosx + 2cos2x
(c) y = cosx + cos2x (d) None
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4 Answers
29Ans 4..mutilply both sides by sec2x .. will get a linear differential equation..ans will be D..
Ans 5 ..that's also a linear diferential equation..
11)b
x2 is not one-one as for a particular value of y,there are 2 corresponding values of x(+ve and -ve of equal magnitude) and also it is not onto as it does not take all real values(only +ve)
2)a
(a*b)*c=1/4(a+b+2c)
a*(b*c)=1/4(2a+b+c)
thus (a*b)*c≠a*(b*c) and the operation is not associative.