The solution of differential equation xdy-ydx=0 represents

Question

The solution of differential equation xdy-ydx=0 represents

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

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Given that, `xdy-ydx=0`
`Rightarrow xdy=ydx`
`Rightarrow (dy)/(y)=(dx)/(x)`
On integrading both sides, we get `log y=log x+logC`
`Rightarrow log y=cos Cx`
`Rightarrow y=Cx`
Which is a straight line passing through origin.

4 views Answered 2023-02-05 15:29