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If y=e^tanx then prove that: cos^2x(d...

If `y=e^tanx` then prove that:
`cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0`

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IF y=e^(tan^(-1)x) then prove that : (1+x^(2))(d^2y)/(dx^2)+(2x-1)(dy)/(dx)=0 .

If y=x+tanx , show that cos^2x\ (d^2y)/(dx^2)-2y+2x=0 .

If y=(sin^(-1)x)^2 then prove that (1-x^(2))(d^2y)/(dx^2)-x(dy)/(dx)-2=0 .

If y="sin"(logx), then prove that (x^2d^2y)/(dx^2)+x(dy)/(dx)+y=0

If x = a cos theta + b sin theta and y =asin theta-b cos theta , then prove that y^2 (d^2y)/(dx^2)-x(dy)/(dx)+y=0

If y=x^x prove that (d^2y)/(dx^2)-1/(y)(dy/dx)^2-y/x=0

If y=e^(ax) sin bx then prove that (d^2y)/(dx^(2))-2a(dy)/(dx)+(a^(2)+b^(2))y=0 .

If y=e^m\ sin^((-1)x) , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2y=0 .

If x=tan(1/a log y) , prove that (1+x^2) (d^2y)/(dx^2)+(2x-a) (dy)/(dx)=0

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NAGEEN PRAKASHAN ENGLISH-Continuity and Differentiability-Exercies 5l
  1. Find the 2nd derivative if x^3 log x with respect to x.

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  2. If y=tan^(-1)x^3 then find (d^2y)/(dx^(2)).

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  3. Find the 2nd dervative of e^(ax+b) with respect to x.

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  4. If y=x+cotx then prove that sin^2x(d^2y)/(dx^2)-2y+2x=0.

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  5. If y=log(sinx) , prove that (d^3y)/(dx^3)=2cosx cos e c^3x .

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  6. If y=Acosn x+Bsinn x ,s howt h a t (d^2y)/(dx^2)+n^2y=0

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  7. (i) If y=asin(log x) then prove that x^(2)*(d^2y)/(dx^2)+x(dy)/(dx)+y=...

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  8. If y=(sin^(-1)x)^2 then prove that (1-x^(2))(d^2y)/(dx^2)-x(dy)/(dx)-2...

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

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  10. IF y=e^(tan^(-1)x) then prove that : (1+x^(2))(d^2y)/(dx^2)+(2x-1)(d...

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

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  12. If y=(t a n^(-1)\ x^2) , show that (x^2+1)^2(d^2\ y)/(dx^2)+2x(x^2+1)(...

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  13. If y=e^tanx then prove that: cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0

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  14. 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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  15. If x=at^2,y=2 at then find (d^2y)/(dx^2).

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  16. If x=a(t-sint), y=a(1-cost) then find (d^2y)/(dx^2).

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  17. If x=sint and y=sinp t , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^...

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  18. If y=(sin^(-1)x)^2+(cos^(-1)x)^2, then prove that (1-x^2)y2-xy(1)-4=0.

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