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Find the second order derivative of the following functions
If `y = Pe^(ax) + Qe^(bx)` show that `(d^2 y)/(dx^2) - (a + b) (dy)/(dx) + aby = 0`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. lf y=3e^(2x) +2e^(3x), prove that d^2y/dx^2 - 5dy/dx +6y =0.

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  2. If y = Ae^(mx) + Be^(nx), Show that (d^2 /dx^2 y)-(m+n)dy/dx+mny = 0

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  3. Find the second order derivative of the following functions If y = P...

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  4. y = 5 cos x - 3 sin x, prove that (d^2 y)/(dx^2) + y = 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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