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If y= Ae^(mx) +Be^(nx), show that (d^(2)...

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

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NCERT TELUGU-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5.7
  1. Find the second order derivatives of the functions given in x^(2)+3x...

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  2. Find the second order derivatives of the functions given x^(20)

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  3. Find the second order derivatives of the functions given . x. cos x

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  4. Find the second order derivatives of the functions given . log x

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  5. Find the second order derivatives of the functions given . x^(3) log...

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  6. Find the second order derivatives of the functions given . e^(x) sin...

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  7. Find the second order derivatives of the functions given in Exercises ...

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  8. Find the second order derivatives of the functions given . tan^(-1) ...

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  9. Find the second order derivatives of the functions given log (log x)...

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  10. Find the second order derivatives of the functions given in Exercises ...

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

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  12. If y= cos^(-1) x, Find (d^(2)y)/(dx^(2)) in terms of y alone.

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  13. If y= 3 cos (log x)+4 sin(log x), show that x^(2)y(2)+xy(1)+y=0.

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

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  15. If y= 500e^(7x) +600e^(-7x), show that (d^(2)y)/(dx^(2))= 49y.

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

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  17. If y= (tan^(-1)x)^(2), show that (x^(2)+1)^(2) y(2)+2x(x^(2)+1)y(1)=2.

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