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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^2 y=0`.

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RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If x=asint and y=a(cost+log tan(t/2) ) , find (d^2y)/(dx^2) .

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  2. lf x=acostheta+bsintheta, y=asintheta-bcostheta then show that y^2(d^...

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

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  4. If x=sintheta , y=cosptheta , prove that (1-x^2)y2-x y1+p^2y=0 , where...

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  5. If (x-a)^2+(y-b)^2=c^2, for some c >0, prove that([1+((dy)/(dx))^2]^(...

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  6. If y^2=a^2cos^2x+b^2sin^2x then prove that (d^2y)/(dx^2)+y=(a^2b^2)/(y...

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  7. If f(x)=|x|^3 , show that f"(x) exists for all real x and find it.

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  8. In (dy)/(dx),\ x is independent variable and y is the dependent ...

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  9. In (dy)/(dx),x is a independent variable and y is the dependent vari...

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  10. Find second order derivative of x^3+tanx

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  11. Find second order derivative of sin(logx)

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  12. Find second order derivative of log(sinx)

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  13. Find second order derivative of e^xsin5x

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  14. Find second order derivative of e^(6x)cos3x

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  15. Find second order derivative of x^3logx

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  16. Find second order derivative of tan^(-1)x

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  17. Find second order derivative of xcosx

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  18. Find second order derivative of log(logx)

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  19. If y=e^(-x)cosx, show that (d^(2)y)/(dx^(2))=2e^(-x)sinx.

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

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