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If y=acos(lnx)+bsin(lnx) then prove that...

If `y=acos(lnx)+bsin(lnx)` then prove that `x^2y_3+3x y_2+2y_1=0`

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BANSAL-LIMITS AND DERIVATIVES-All Questions
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  2. If y=sin(sinx) then prove that y2+(tanx)y1+ycos^2x=0

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  3. If y=acos(lnx)+bsin(lnx) then prove that x^2y3+3x y2+2y1=0

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  4. If y=e^acos^((-1)x) , then prove that (1-x^2)y2-x y1-a^2y=0 .

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  5. If (x-a)^2+(y-b)^2=c^2\ \ (c >0) then ([1+((dy)/(dx))^2]^(3//2))/((d^2...

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

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

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

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

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

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

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

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

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