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Show that x y=a e^x+b e^(-x)+x^2 is a so...

Show that `x y=a e^x+b e^(-x)+x^2` is a solution of the differential equation `x(d^2y)/(dx^2)+2dy/dx-x y+x^2-2=0.`

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RD SHARMA ENGLISH-DIFFERENTIAL EQUATION-All Questions
  1. Form the differential equation representing the family of ellipses ...

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  2. Form the differential equation representing the family of ellipses ...

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  3. Show that x y=a e^x+b e^(-x)+x^2 is a solution of the differential equ...

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  4. Verify thaty=c x+2c^2 is a solution of the differential equation 2((dy...

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  5. Show that y^2-x^2 - x y=a is a solution of the differential equation (...

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  6. Verify that y=A\ cos x+sinxsatisfies the differential equation cosx \ ...

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  7. Find the differential equation corresponding to y=a e^(2x)+b e^(-3x)+c...

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  8. The differential equation of all parabolas whose axis are parallel ...

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  9. From x^2+y^2+2a x+2b y+c=0, derive a differential equation not contain...

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  10. Solve: (dy)/(dx)=sin^3x \ cos^4x+x\ sqrt(x+1)

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  11. Solve the differential equation: (dy)/(dx)=y^2+2y+2

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  12. Solve the following differential equation: (dy)/(dx)=x^2e^x

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  13. Solve the differential equation: tany\ dx+tanx\ dy=0

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  14. Solve the differential equation: x \ cos^2y\ dx=y \ cos^2x\ dy

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  15. Solve: (ln(secx+tanx)/(cosx))dx=(ln(secy+tany)/(cosy))dy

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  16. Solve the following differential equation: \ cos e c\ xlogy(dy)/(dx)+\...

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  17. Solve the differential equation: (dy)/(dx)=1/(x^2+4x+5)

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  18. Solve the differential equation: (dy)/(dx)+\ 4x=e^x

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  19. Solve the following differential equation: (dy)/(dx)-xsin^2x=1/(xlogx)

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  20. Solve the following differential equations: (x+2)(dy)/(dx)-x^2+4x-9,x...

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