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The general solution of the differenti...

The general solution of the differential equation `(y dx-x dy)/y=0` is
(A) `x y" "=" "C` (B) `x=C y^2` (C) `y" "=" "C x` (D) `y=C x^2`

A

`xy=C`

B

`x=Cy^(2)`

C

`y=Cx`

D

`y=Cx^(2)`

Text Solution

Verified by Experts

Given differential equation is `(ydx-xdy)/(y)=0`
`implies ydx-xdy=0 implies (1)/(x)dx-(1)/(y)dy=0`
On integration, `log|x|-log|y|=logk`
`implies log|(x)/(y)|=logkimplies(x)/(y)=k`
` y=(1)/k)ximpliesy=Cx` (Let `(1)/(k)=C`)
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NAGEEN PRAKASHAN ENGLISH-DIFFERENTIAL EQUATIONS-Miscellaneous Exercise
  1. For each of the differential equations given below, indicate its orde...

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  2. For each of the exercises given below, verify that the given function...

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

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  4. Prove that x^2-y^2=c(x^2+y^2)^2 is the general solution of differe...

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  5. Form the differential equation of the family of circles in the firs...

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  6. Find the general solution of the differential equation (dy)/(dx)+sqrt...

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  7. Show that the general solution of the differentia equation (dy)/(dx...

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

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

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  10. Solve the differential equation y e^(x/y)dx=(x e^(x/y)+y^2)dy(y!=0)

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

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  12. Solve the differential equation [(e^(-2sqrt(x)))/(sqrt(x))-y/(sqrt(x)...

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  13. Find the particular solution of the differential equation. (dy)/(dx...

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  14. find the particular solution satisfying the given condition, for the f...

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  15. The population of a village increases continuously at the rate prop...

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

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

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  18. Solve: e^(x)(x+1)dx+(ye^(y)-xe^(x))dy=0, such that f(0)=0

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