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If y = A sinx + B cosxthen prove that d^...

If `y = A sinx + B cosx`then prove that `d^2y/dx^2 + y = 0`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. y = 5 cos x - 3 sin x, prove that (d^2 y)/(dx^2) + y = 0

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  2. If e^y(x+1)=1 show that (d^2y/dx^2) = (dy/dx)^2 ਹੈ।

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  3. If y = A sinx + B cosxthen prove that d^2y/dx^2 + y = 0

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  4. Find (d^2)/(dx^2) in the following : x = at^2, y = 2 at

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  5. Find (d^2)/(dx^2) in the following : x = a costheta, y = b sin theta

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  6. Find (d^2)/(dx^2) in the following : x = a cos^3 theta, y = a sin^3t...

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  7. Find (d^2y)/(dx^2) in the following x = a cos^3 theta, y = a sin^3 t...

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  8. Find (d^2)/(dx^2) in the following : If x = a cos^3 theta and y = a ...

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  9. Find (d^2)/(dx^2) in the following : x = a (cost + t sin t), y = a (...

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  10. Find (dy^2)/(dx^2) in the following : x = a (theta - sin theta), y =...

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  11. Find (d^2y)/(dx^2) at theta = pi/2 when: x = a (theta-sintheta),y=a(...

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  12. Find (d^2y)/(dx^2) at theta = pi/2 when: x=a(1-costheta), y = a(thet...

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  13. Find (d^2y)/(dx^2) at theta = pi/2 when: x=a(theta - sin theta), y =...

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  14. Find (d^2y)/(dx^2) when : x=2 cos theta - cos 2theta and y = 2 sin the...

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  15. If x = a sin t and y = a (cos t + log tan (t/2)), find (d^2y)/(dx^2)

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  16. If y = (sin^-1 x)^2, then prove that (1 -x)^2 (d^2y)/(dx^2) -x dy/dz =...

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  17. If y = (cos^-1 x)^2 show that (1-x^2)^2 y2 -xy1 = 2

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  18. If y=[tan^-1 x]^2, then prove that : (x^2 + 1)^2 y2+2x(x^2+1) y1 = 2.

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  19. Verify the truth of Rolle's Theorem for the following functions: f(x...

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  20. Verify the truth of Rolle's Theorem for the following functions: f(x...

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