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If y=3cos(logx)+4sin(logx),\ then show ...

If `y=3cos(logx)+4sin(logx),\ ` then show that `x^2dot(d^2\ y)/(dx^2)+(dy)/(dx)+y=0`

A

` -y `

B

` y`

C

` -12y`

D

` 12y`

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The correct Answer is:
A
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NIKITA PUBLICATION-DIFFERENTIATION -MCQ
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  2. If y="sin"(sinx),"p r o v et h a t" (d^2y)/(dx^2)+tanx(dy)/(dx)cos^...

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  3. If y=3cos(logx)+4sin(logx),\ then show that x^2dot(d^2\ y)/(dx^2)+...

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  4. If y= cos ec x -cot x ,then sin x (d^(2)y)/(dx^(2))=

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  5. If y=sin(log(e)x), then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx) is equal to

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  6. If y=cos (log x) ,then " "x^(2) (d^(2)y)/(dx^(2))+x(dy)/(dx)=

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  7. If y=sin (msin ^(-1) x),then (1-x^(2))(d^(2)y)/(dx^(2))-x( dy)/(dx)=

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  8. If y=sin(mcos^(-1)x),"show that "(1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)...

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  9. If y=cos (mcos ^(-1) x ),then (1-x^(2)) (d^(2)y)/(dx^(2) )-x( dy)/(dx)...

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  10. If y= sin (mlog (x+ sqrt( 1+x^(2)))),then (1+x^(2) ) (d^(2)y)/(dx^(2)...

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  11. If y=a cos ( log x )+ bsin (log x) where a ,b are parameters ,then ...

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  13. If u=A e ^(mx) +Be^(nx ) ,then y2-( m+n) y1+ mn y=

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  14. If y= e ^(mcos ^(-1)x) ,then (1-x^(2) ) (d^(2)y)/(dx^(2)) -x(dy)/(dx)...

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  15. If y= x^(2) e^(x) ,then ( d^(2)y)/(dx^(2)) -(dy)/(dx) =

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  16. If e^(y) (x+1) =1,then y2=

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  17. (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

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  18. "If "y= xlog ((x)/(a+bx))," then "x^(3)(d^(2)y)/(dx^(2))=

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  19. If y=log (log 2x) ,then x ( d^(2)y)/(dx^(2))+(dy)/(dx) =

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

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