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Show that the differential equation 2y ...

Show that the differential equation `2y e^(x/y)dx+(y-2x e^(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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MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-EXERCISE 9 (h) Long Answer Type Questions (I)
  1. Solve the following differential equations : (x+y)dy+(x-y)dx=0, g...

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  2. Solve the following differential equations : x^(2)dy=(2xy+y^(2))dx,...

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  3. Solve : x (dy)/(dx)-y=sqrt(x^(2)+y^(2)), x!=0

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  4. Solve x\ dy-y\ dx=sqrt(x^2+y^2)dx

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  5. x(dy)/(dx)-y+xsiny/x=0

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  6. (xcosy/x)(dy)/(dx)=(ycosy/x)+x

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  7. Show that the following differential equations are homogeneous and sol...

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  8. Show that the given differential equation is homogeneous and solve ea...

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  9. Solve the following differential equations (x dy -y dx)y sin (y/x)= ...

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  10. Find the particular solution of eh differential equation (dy)/(dx)=...

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  11. Find the particular solution of the differential equation {xsin^(2)y/x...

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  12. Find the particular solution of the differential equation x(dy)/(dx)=y...

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  13. Show that the differential equation x(dy)/(dx)sin(y/x)+x-ysin(y/x)=0 i...

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  14. Find the particular solution of the differential equation (xe^(y//x)+y...

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  15. Show that the differential equation 2y e^(x/y)dx+(y-2x e^(x/y))dy=0 i...

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  16. Find the particular solution of the differential equation : (x dy - ...

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  17. (dy)/(dx)=(y)/(x)+tan((y)/(x))

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  18. Solve: x (dy)/(dx)- y-x tan . (y/x). = 0

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  19. Show that the family of curves for which the slope of the tangent a...

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  20. Show that the family of curves for which the slope of the tangent a...

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