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Show that the differential equation 2ye^...

Show that the differential equation `2ye^(x)/(y) dx + ( y - 2xe^(x)/(y)) dy = 0` is homogeneous and find its particular solution, given that, x = 0 when y = 1.

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The correct Answer is:
`2e^(x)/(y) + log |y| = 2`
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NCERT BANGLISH-DIFFERENTIAL EQUATIONS-MISCELLANEOUS EXERCISE
  1. Show that the differential equation 2ye^(x)/(y) dx + ( y - 2xe^(x)/(y)...

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  2. For each of the differential equations given below, indicate its order...

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  3. show that if. y = sin 3x : then(d^(2)y)/(dx^(2)) + 9y = 0

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  4. Form the differential equation representing the family of curves give...

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  5. Prove the x^(2) - y^(2) = c (x^(2) + y^(2))^(2) is the general solutio...

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  6. Form the differential equation of the family of circles in the first q...

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  7. Find the general solution of the differential equation (dy)/(dx) + sqr...

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  8. Show that the general solution of the differential equation (dy)/(dx) ...

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  9. Find the equation of the curve passing through the point (0, (pi)/(4))...

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  10. Find the particular solution of the differential equation (1 + e^(2x)...

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  11. Solve the differential equation y dx = (x + y^(2))dy ( y ne 0).

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  12. Find a particular solution of the differential equation (x - y)(dx + d...

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  13. Solve the differential equation [(e^(-2sqrtx))/(sqrtx) - (y)/(sqrtx)](...

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  14. Find a particular solution of the differential equation (dy)/(dx) + y...

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  15. Find a particular solution of the differential equation (x + 1)(dy)/(d...

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  16. The population of a village increases continuously at the rate propor...

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

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  18. The general solution of a differential equation of the type (dy)/(dx)...

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  19. The general solution of the differential equation e^(x) dy + (y e^(x) ...

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