Home
Class 12
MATHS
Solution of the differential equation xd...

Solution of the differential equation `xdy-ydx=0` represents

A

Rectangular hyperbola

B

Straight line passing through (0,0)

C

Parabola with vertex at (0,0)

D

Circle with centre at (0,0)

Text Solution

Verified by Experts

The correct Answer is:
B
Given that x dy - ydx =0
Dividing both the sides by ` x^(2)`
`Rightarrow (xdy -ydx)/(x^(2)) =0`
` Rightarrow d( y/x) =0`
` Rightarrow y/x =c Rightarrow y =cx`, where c is a constant
Thus it a straight line passing through (0,0)
Aliter :
Given , xdy -ydx =0
` Rightarrow (dy)/y = (dx)/x `
Integrating both the sides , ` int (dy)/y = int (dx)/x + log c `
`log y = log x + log c` where c is constant
`Rightarrow y = cx`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DERIVATIVES

    NDA PREVIOUS YEARS|Exercise MCQs|94 Videos

  • FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY

    NDA PREVIOUS YEARS|Exercise MCQs|232 Videos

Similar Questions

Explore conceptually related problems

The solution of the differential equation ydx-xdy=xydx is

The solution of the differential equation ydx-xdy+xy^(2)dx=0, is

Knowledge Check

  • The solution of differential equation xdy-ydx=0 represents

    A
    a reactangular hyperbola
    B
    parabola whose vertex is at orgin
    C
    straight line passing through origin
    D
    a circle whose centre is at origin

  • What is the solution of the differential equation xdy-ydx=xy^2 dx ?

    A
    `yx^2+2x=2Cy`
    B
    `y^2+2y=2Cx`
    C
    `y^2x^2+2x=2Cy`
    D
    None of the above

  • The solution of the differential equation xdy-ydx = sqrt(x^2+y^2) dx is :

    A
    `x+sqrt(x^2+y^2) = cx^2`
    B
    `y-sqrt(x^2+y^2) = cx`
    C
    `x-sqrt(x^2+y^2) = cx`
    D
    `y+sqrt(x^2+y^2) = cx^2`

    • Similar Questions

    Explore conceptually related problems

    The solution of the differential equation xdy-ydx = sqrt(x^2+y^2) dx is :

    Solution of the differential equation ydx-x dy+logx dx=0 is

    The solution of the differential equation xdy + (x+y) dx=0 is

    What is the general solution of the differential equation x dy -ydx = y^(2) ?

    The solution of the differential equation (1+xy)xdy+(1-xy)ydx=0 ,is

    Home
    Profile