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Solve each of the following initial valu...

Solve each of the following initial value problem: `2x^2(dy)/(dx)-2x y+y^2=0,\ y(e)=e`

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The correct Answer is:
`y=(2x)/(1+|log x|), (x !=0, pm 1/e)`
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MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-EXERCISE 9 (h) Long Answer Type Questions (I)
  1. Find the particular solutions of the following problems : x^(2)dy-(x...

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  2. Solve the following differential equation: (x^2-y^2)dx+2x y\ dy=0 gi...

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  3. Solve each of the following initial value problem: 2x^2(dy)/(dx)-2x y+...

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

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  5. Solve each of the following initial value problem: x e^(y//x)y+x(dy)/(...

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  6. Solve each of the following initial value problems: (x e^(y//x)+y)d...

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  7. Solve the following differential equation: (x-y)(dy)/(dx)=x+2y

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  8. Solve the following differential equations : (x+y)dy+(x-y)dx=0, g...

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

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

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

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

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

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

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

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

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

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

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

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

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