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Show that the family of curves for which...

Show that the family of curves for which the slope of the tangent at any point (x, y) on it is `(x^2+y^2)/2xy`, is given by `x^2-y^2 = cx`

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The correct Answer is:
`x^(2) - y^(2) =cx`
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OMEGA PUBLICATION-DIFFERENTIAL EQUATIONS-MULTIPLE CHOICE QUESTIONS (MCQs)
  1. Show that the family of curves for which the slope of the tangent at a...

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  2. The degree of the differential equation ((d^(2)y)/(dx^(2)))^(3) + ((...

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  3. The degree of differential equation: (d^(4)y)/(dx^(4)) + sin (y''')=...

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  4. The number of arbitrary constants in the general solution of a differe...

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  5. The order of the differential equation: 2x^(2) (d^(2)y)/(dx^(2)) - 3...

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  6. The order of the differential equation: (y''')^(2) + (y'') + (y')^(4...

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  7. The number of arbitrary constants in the particular solution of a diff...

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  8. Which of the following differential equations hasy=c(1)e^(x) + c(2)e^(...

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  9. Which of the following differential equation has y = x as one of its p...

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  10. A homogeneous differential equation of the form (dx)/(dy) = h(x/y) ca...

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  11. Which of the following is a homogeneous differential equation?

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  12. The integrating factor of the differential equation x(dy)/(dx) - y =...

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  13. The integrating factor of the differential equation (1-y^(2))(dx)/(d...

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  14. The general solution of the differential equation (y dx - x dy)/y = 0 ...

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  15. The general solution of the differential equation of the type: (dx)/...

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  16. The general solution of the differential equation e^(x)dy + (ye^(x) + ...

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  17. The integrating factor of x(dy)/(dx) + 2y = x^(2) is:

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  18. Solve the following differential equations (dy)/( dx) - y = cos x

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  19. The degree of differential equation: (d^(2)y)/(dx^(2)) = y +((dy)/(d...

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  20. The degree of the differential equation 3(d^(2)y)/(dx^(2)) + 4((dy)/...

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  21. The degree of the differential equation (d^(2)y)/(dx^(2))+3((dy)/(dx...

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