" Q.15.Differenitate "x^(x)-2^(sin x)

Show that , the solution x = e^(-kt) (a cos nt + b sin nt ), for all a and b , always satisfies the differenital equation (d^(2)x)/(dt^(2)) + 2k (dx)/(dt) + (k^(2) + n^(2)) x = 0

The solution of the differenital equation (dy)/(dx) = (x +y)/(x) satisfying the condition y(1) = 1 is

Find the derivative of (a x^2 + sin x)(p + q cos x)

The differenital equation representing the family of curves y =a sin (lambdax +alpha) is :

If range of the function f(x)=(2sin^(2)x+2sin x+3)/(sin^(2)x+sin x+1)is[p,q], then the value of 3p+6q+1 is (10)/(3) (b) (7)/(3)(c)28 (d) None of these

int_( is equal to )^( Let )(cos^(3)x+cos^(5)x)/(sin^(2)x+sin^(4)x)dx=p sin x-(9)/(sin x)-r tan^(-1)(sin x)+Cthenp+2q+

If p = cos x - sin x, q = (1 - sin ^(3) x)/( 1 - sin x) , r = (1 + cos ^(3) x)/( 1 + cos x) what is the value of p + q + r ?

Prove that (sin x-sin 3 x)/(sin ^(2) x-cos ^(2) x)=2 sin x

Find the differenital equation for the curve y=k(x-k)^(2) for all values of k .