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If y=e^(asin^(-1)x) then show that (1-x^...

If `y=e^(asin^(-1)x)` then show that `(1-x^2)y_(n+2)-(2n+1)xy_(n+1)-(n^2+a^2)y_n=0`

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BANSAL-LIMITS AND DERIVATIVES-All Questions
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  2. If y=e^tan^((-1)x) , prove that (1+x^2)y2+(2x-1)y1=0 .

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  3. If y=e^(asin^(-1)x) then show that (1-x^2)y(n+2)-(2n+1)xy(n+1)-(n^2+a^...

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  5. Find (dy)/(dx) , if x=a t^2 , y=2a t

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  6. Find (dy)/(dx) , if x^(2/3) +y^(2/3)=a^(2/3)

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  7. Find (dy)/(dx) , if x=2a t^2 , y=a t^4

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  8. Find (dy)/(dx) , if x=(sin^3t)/(sqrt(cos2t)) , y=(cos^3t)/(sqrt(cos2t)...

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  9. Find (dy)/(dx) , if x=acostheta , y=bcostheta

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  10. Find (dy)/(dx) , if x=costheta-cos2theta , y=sintheta-sin2theta

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  11. Find (dy)/(dx), when x=a e^(theta)(sintheta-costheta),y=a e^(theta)(si...

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  12. Find (dy)/(dx) , if x=a(cost+logtant/2) , y=asint

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  13. Find (dy)/(dx) , if x=asectheta , y=btantheta

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  14. Find (dy)/(dx) , if x=a(costheta+thetasintheta) , y=a(sintheta-thetaco...

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  15. If x=sqrt(a^sin^((-1)t)) , y=sqrt(a^cos^((-1)t)) , show that (dy)/(...

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

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  19. If y=5cosx-3sinx , prove that (d^2y)/(dx^2)+y=0 .

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

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