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If y=A e^(-k t)cos(p t+c), then prove th...

If `y=A e^(-k t)cos(p t+c),` then prove that `(d^2y)/(dt^2)+2k(dy)/(dx)+n^2y=0` , where `n^2=p^2+k^2`

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RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If x=asint-bcost ,\ \ y=acost+bsint ,find (dy)/(dx) .

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  2. Find A\ a n d\ B so that y=Asin3x+Bcos3x satisfies the equation (d^2y)...

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  3. If y=A e^(-k t)cos(p t+c), then prove that (d^2y)/(dt^2)+2k(dy)/(dx)+n...

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  4. If y=acos(logx) , find (dy)/(dx) .

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  5. If y=a[x+(x^2-1)^(1/2)]^n+b[x-(x^2-1)^(1/2)]^n the value of the expre...

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  6. If y=a\ x^(n+1)+b x^(-n) find (dy)/(dx) .

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  7. If x=acosn t-bsinn t and (d^2x)/(dt^2)=lambdax , then find the value ...

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  8. If x=t^2 and y=t^3 , find (d^2y)/(dx^2) .

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  9. If x=2a t , y=a t^2 , where a is a constant, then find (d^2y)/(dx^2...

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  10. If x=f(t) and y=g(t) , then write the value of (d^2y)/(dx^2) .

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  11. If y=1-x+(x^2)/(2!)-(x^3)/(3!)+(x^4)/(4!)dotto\ oo , then write (d^2y)...

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  12. If y=x+e^x , find (d^2x)/(dy^2) .

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  13. If y=(x-x^2) , then find (d^2y)/(dx^2) .

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  14. If y=log x , find (d^2y)/(dx^2) .

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  15. If x=acosn t-bsinn t , then find (dx)/(dt)

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  16. If x=a t^2,\ \ y=2\ a t , then find (dy)/(dx)

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  17. If y=a x^(n+1)+b x^(-n) , then x^2(d^2y)/(dx^2)= n(n-1)y (b) n(n+1)y ...

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  18. (d^(20))/(dx^(20))(2cosxcos3x)= 2^(20)(cos2x-2^(20)cos4x) (b) 2^(20)(...

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  19. If x=t^2,\ \ y=t^3 , then (dy)/(dx)

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  20. If y=a+b x^2,\ a ,\ b arbitrary constants, then find dy/dx

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