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- Prove that the trial solution of 2nd order homogeneous linear ( ODE ) with constant coefficients in the case of real double roots (λ= -a/2 ) is equal to : y(x)= (c1+ c2 * x ) e^((-a/2)*x) subject :- sconde orderCalculate ∂ω∂z for ω=ze(xy2+2z).The integral of the given function ∫csc^6(x) dx is equal to a. 3cos^5x -10sin^2x cos^3x -15sin^4x cosx/15sin^5x + C b.3cos^5 x+x cos^3x -15sin^4x cosx/15sin^5x + C c. 3cos^5x -10sin^2x cos^3x -15sin^4x cosx/5sin^5x + C d. 3cos^5x +10xcos^3x -15sin^4x cosx/5sin^5 x + C