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If y=[log(x+sqrt(x^2+1))]^2, show that, ...

If `y=[log(x+sqrt(x^2+1))]^2`, show that,
`(1+x^2)(d^2y)/(dx^2)+xdy/dx=2`

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CHHAYA PUBLICATION-SECOND ORDER DERIVATIVE-Short Answer type Question
  1. If y=x^3log""1/x, Prove that , xy2-2y1+3x^2=0.

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  2. If y=log(x+sqrt(x^2+a^2)), show that (a^2+x^2)y2+xy1=0

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  3. If y=[log(x+sqrt(x^2+1))]^2, show that, (1+x^2)(d^2y)/(dx^2)+xdy/dx=...

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  4. IF y=secx+tanx, show that , y2-yy1=0.

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  5. If y=3cos(logx)+4sin(logx), Prove that x^2y2+xy1+y=0

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  6. IF y=xsin(logx)+xlogx, Prove that, x^2(d^2y)/(dx^2)-xdy/dx+2y=2xlogx

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  7. IF y=x^2cosx, prove that ,x^2y2-4xy1+(x^2+6)y=0.

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  8. If cosx=ycos(a+x), prove that, (d^2y)/(dx^2)=2sinasec^2(a+x)tan(a+x)

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  9. If y=sin(logx), prove that , x^2y2+xy1+y=0.

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  10. If logy=sin^-1x, show that, (1-x^2)(d^2y)/(dx^2)=xdy/dx+y.

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  11. IF y=cos(cos x), show that, y2-y1cotx+ysin^2x=0.

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  12. If y=sin^-1x, show that, (1-x^2)y2-xy1=0.

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  13. If y=(sin^(-1) x)/(sqrt(1-x^2)), then show that (1-x^2)(d^2y)/(dx^2)-3...

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  14. IF x=(a+bt)e^(-nt), show that , (d^2x)/(dt^2)+2ndx/dt+n^2x=0.

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  15. If y=tan^-1x, prove that , (x^2+1)(d^2y)/(dx^2)+2xdy/dx=0.

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

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  17. If y=e^(msin^-1x)(-1lexle1), Prove that, (1-x^2)(d^2y)/(dx^2)-xdy/dx...

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  18. IF y=cos (msin^-1x), prove that ,(1-x^2)y2-xy1+m^2y=0.

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  19. If y=sin (2sin^-1x), Prove that, (1-x^2)(d^2y)/(dx^2)=xdy/dx-4y.

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  20. IF y=3e^(2x)+2e^(3x), show that, y2-5y1+6y=0.

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