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Question
Solve the following differential equation:
`"y" - "x" "dy"/"dx" = 0`
Solution
`"y" - "x" "dy"/"dx" = 0`
∴ `"x" "dy"/"dx" = "y"`
∴ `1/"x" "dx" = 1/"y" "dy"`
Integrating both sides, we get
`int 1/"x" "dx" = int 1/"y" "dy"`
∴ log |x| = log |y| + log c
∴ log |x| = log |cy|
∴ x = cy
This is the general solution.
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