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If y=a e^(2x)+b e^(-x) , show that, (d^2...

If `y=a e^(2x)+b e^(-x)` , show that, `(d^2y)/(dx^2)-(dy)/(dx)-2y=0` .

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(k) (LONG ANSWER TYPE QUESTIONS (I))
  1. If y=cos^(-1)x, then show that : (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx=0

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  2. If y=asin^(-1)x, then show that : (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx=...

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  3. If y=a e^(2x)+b e^(-x) , show that, (d^2y)/(dx^2)-(dy)/(dx)-2y=0 .

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  4. If y=3\ e^(2x)+2\ e^(3x) , prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0 .

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  5. If y=A e^(m x)+B e^(n x), show that (d^2y)/(dx^2)-((m+n)dy)/(dx)+m n y...

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  6. If y=Pe^(ax)+Qe^(bx), show that : (d^(2)y)/(dx^(2))-(a+b)dy/dx+aby=0...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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