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Question
The general solution of the differential equation ydx – xdy = 0; (Given x, y > 0), is of the form
(Where 'c' is an arbitrary positive constant of integration)
Options
xy = c
x = cy2
y = cx
y = cx2
Solution 1
y = cx
Explanation:
ydx – xdy = 0
`\implies (ydx - xdy)/y^2` = 0
`\implies d(x/y)` = 0
`\implies` x = `1/c y`
`\implies` y = cx.
Solution 2
y = cx
Explanation:
ydx – xdy = 0
`\implies` ydx = xdy
`\implies dy/y = dx/x`; on integrating `int dy/y = int dx/x`
loge |y| = loge |x| + loge |c|
Since x, y, c > 0, we write loge y = loge x + loge c
`\implies` y = cx.
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