`y=e^(x)(a cos x + b sin x)`

Obtain the differential equation by eliminating 'a' and 'b' from the equation : y= e^(x)(a cos 2x + b sin 2x) .

The differential equation of the family of curves y=e^(2x)(a cos x+b sin x) where, a and b are arbitrary constants, is given by

Form the differential equations by eliminating the arbitrary constants from the following equations : 1. (1) xy = Ae^(x) + Be^(-x) + x^(2) (2) y= e^(-x) (A cos 2x + B sin 2x)

If y = tan^(-1) ((a cos x - b sin x)/(b cos x + a sin x)) " then " (dy)/(dx) = ?

y=tan^(-1)((a cos x-b sin x)/(b cos x+a sin x)), where -(pi)/(2) -1

Eliminate 'a' and 'b' from : y= a cos x + b sin x .

y=a cos x+b sin x+x sin x is a solution of the D.E. A) y_(2)+y=x cos x B) y_(2)+2y=2cos x C) y_(2)+y=2cos x D) y_(2)-y=2cos x

Delta (x) = det [[sin2x, e ^ (x) sin x + x cos x, sin x + x ^ (2) cos xcos x + sin x, e ^ (x) + x, 1 + x ^ ( 2) e ^ (x) cos x, e ^ (2) x, e ^ (x)]]

Delta (x) = det [[sin2x, e ^ (x) sin x + x cos x, sin x + x ^ (2) cos xcos x + sin x, e ^ (x) + x, 1 + x ^ ( 2) e ^ (x) cos x, e ^ (2) x, e ^ (x)]]