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If y=(cot^(-1)x)^2 , prove that y2(x^2+1...

If `y=(cot^(-1)x)^2` , prove that `y_2(x^2+1)^2+2x(x^2+1)y_1=2` .

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RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If y=sin(logx) , prove that x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0 .

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  2. If y=3\ e^(2x)+2\ e^(3x) , prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0 .

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  3. If y=(cot^(-1)x)^2 , prove that y2(x^2+1)^2+2x(x^2+1)y1=2 .

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  4. If y="cosec"^(-1)x ,\ \ x >1 , then show that x(x^2-1)(d^2y)/(dx^2)+(2...

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  5. If x=cost+logtan(t/2),\ \ y=sint , then find the value of (d^2y)/(dt^2...

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  6. If x=asint and y=a(cost+logtan(t/2)) , find (d^2y)/(dx^2) .

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  7. If x=a(cost+tsint) and y=a(sint-tcost) , then find the value of (dy)...

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  8. If x=a(cost+logtan(t/2)) , y=asint , evaluate (dy)/(dx) .

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  9. If x=a(cos2t+2tsin2t) and y=a(sin2t-2tcos2t) , then find (dy)/(dx) .

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  10. If x=asint-bcost ,\ \ y=acost+bsint ,find (dy)/(dx) .

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

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

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

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

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

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

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

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

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