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Question
The general solution of the differential equation y dx – x dy = 0 is ______.
Options
xy = C
x = Cy2
y = Cx
y = Cx2
Solution
The general solution of the differential equation y dx – x dy = 0 is y = Cx.
Explanation:
y dx – x dy = 0
⇒ y dx – x dy = 0
⇒ `(dy)/y = (dx)/x`
⇒ `int (dy)/y = int (dx)/x + logK, K > 0`
⇒ log |y| = log |x| + log K
⇒ log |y| = log |x| K
⇒ |y| = |x| K
⇒ y = ± Kx
⇒ y = Cx
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