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If e^y(x+1)=1,s howt h a t(d^2y)/(dx^2)=...

If `e^y(x+1)=1,s howt h a t(d^2y)/(dx^2)=((dy)/(dx))^2dot`

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If e^y(x+1)=1 . Show that (d^2y)/(dx^2)=((dy)/(dx))^2

If e^(y)(x+1)=1 ,show that (d^(2)y)/(dx^(2))=((dy)/(dx))^(2)

If e^(y)(x+1)=1, show that (d^(2)y)/(dx^(2))=((dy)/(dx))^(2)

If e^(y)(x+1)=1, show that (d^(2)y)/(dx^(2))=((dy)/(dx))^(2) If y=sin(2sin^(-1)x), show that ((1-x^(2))d^(2y))/(dx^(2))=x(dy)/(dx)-4y

If y=x^(2)e^(x),"show that "(d^(2)y)/(dx^(2))-(dy)/(dx)-2(x+1)e^(x)=0

If y=e^(x)sinx, prove that (D^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0 .

Q.if log y=sin^(-1)x, show that,(1-x^(2))((d^(2)y)/(dx^(2)))=x((dy)/(dx))+y

If sqrt(y+x)+sqrt(y-x)=c ,s howt h a t(dy)/(dx)=y/x-sqrt((y^2)/(x^2)-1.)

If sqrt(y+x)+sqrt(y-x)=c ,s howt h a t(dy)/(dx)=y/x-sqrt((y^2)/(x^2)-1.)

If y=e^acos^((-1)x) , -1lt=xlt=1 , show that (1-x^2) (d^2y)/(dx^2)-x(dy)/(dx)-a^2y=0 .

MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(k) (LONG ANSWER TYPE QUESTIONS (I))
  1. If y=2sinx+3cosx, prove that : y+(d^(2)y)/(dx^(2))=0

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

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  3. If e^y(x+1)=1,s howt h a t(d^2y)/(dx^2)=((dy)/(dx))^2dot

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  4. If y=Asinx+Bcosx, prove that (d^(2)y)/(dx^(2))+y=0.

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  5. Find (d^(2)y)/(dx^(2)) in the following x=at^(2),y=2at

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  6. Find (d^(2)y)/(dx^(2)) in the following x=(2at^(2))/(1+t),y=(3at)/(1...

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  7. Find (d^(2)y)/(dx^(2)) in the following x=acostheta,y=bsintheta

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  8. Find (d^(2)y)/(dx^(2)) in the following x=acos^(3)theta,y=asin^(3)th...

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  9. Find (d^(2)y)/(dx^(2)) in the following x=acos^(3)theta,y=bsin^(3)th...

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  10. Find (d^(2)y)/(dx^(2)) in the following If x^(2/3)+y^(2/3)=a^(2/3),"...

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  11. Find (d^(2)y)/(dx^(2)) in the following If x=acos^(3)thetaandy=asin^...

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  12. Find (d^(2)y)/(dx^(2)) in the following x=a(cost+tsint),y=a(sint-tco...

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  13. Find (d^(2)y)/(dx^(2)) in the following x=a(theta+sintheta),y=a(1+co...

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  14. Find (d^(2)y)/(dx^(2))" at "theta=pi/2 when : x=a(theta+sintheta),y=...

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  15. Find (d^(2)y)/(dx^(2))" at "theta=pi/2 when : x=a(theta-sintheta),y=...

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  16. Find (d^(2)y)/(dx^(2))" at "theta=pi/2 when : x=a(1-costheta),y=a(th...

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  17. Find (d^(2)y)/(dx^(2))" at "theta=pi/2 when : x=a(theta-sintheta),y=...

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  18. Find (d^(2)y)/(dx^(2))" at "theta=pi/4 when : x=a(costheta+logtanthe...

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  19. If x=cost+logtant/2,\ \ y=sint , then find the value of (d^2y)/(dt^2) ...

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  20. Find (d^(2)y)/(dx^(2)) when : x=2costheta-cos2thetaandy=2sintheta-si...

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