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If x=sint ,y=sinpt, prove that (1-x^2...

If `x=sint ,y=sinpt`, prove that `(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2y=0.`

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If x=sint,y=sinpt , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2 y=0 .

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RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If x=costheta , y=s in^3theta , prove that y\ (d^2y)/(dx^2)+((dy)/(dx)...

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  2. If y=sin(sinx) , prove that (d^2y)/(dx^2)+tanxdot(dy)/(dx)+y\ cos^2x=0...

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  3. If x=sint ,y=sinpt, prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2y...

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  4. If y=(sin^(-1)x)^2 , prove that (1-x^2)y2-x y1-2=0 .

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  5. If y=e^(tan^(-1)x) , prove that (1+x^2)y2+(2x-1)y1=0 .

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  6. If y=3cos(logx)+4sin(logx),\ prove that x^2y2+x\ y1+y=0 .

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  7. If y=e^(2x)(a x+b) , show that y2-4\ y1+4\ y=0 .

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  8. If x=sin(1/alogy) , show that (1-x^2)y2-x\ y1-a^2\ y=0 .

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  9. If logy=tan^(-1)x , show that (1+x^2)y2+(2x-1)y1=0 .

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  10. If y=tan^(-1)x , show that (1+x^2)(d^2y)/(dx^2)+2x(dy)/(dx)=0 .

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  11. If y={log(x+sqrt(x^2+1))}^2 , show that (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx...

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  12. If y=(tan^(-1)x)^2 , then prove that (1+x^2)^2\ y2+2x\ (1+x^2)y1=2 .

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  13. If y=cotx show that (d^2y)/(dx^2)+2y(dy)/(dx)=0 .

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  14. Find (d^2y)/(dx^2) , where y=log((x^2)/(e^2)) .

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  15. If y=a e^(2x)+b e^(-x) , show that, (d^2y)/(dx^2)-(dy)/(dx)-2y=0 .

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  16. If y=e^x(sinx+cosx) prove that (d^2y)/(dx^2)-2(dy)/(dx)+2y=0 .

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

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  18. If y=e^(acos^(-1)x) , -1lt=xlt=1 , show that (1-x^2) (d^2y)/(dx^2)-x...

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

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  20. If x=2cost-cos2t ,\ \ y=2sint-sin2t , find (d^2y)/(dx^2) at t=pi/2 .

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