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Question
The general solution of the differential equation `dy/dx = e^(x+y)` is ______.
Options
ex + e-y = C
ex + ey = C
e-x + ey = C
e-x + e-y = C
Solution
The general solution of the differential equation `dy/dx = e^(x+y)` is ex + e-y = C.
Explanation:
`dy/dx = e^x + y = e^x * e^y`
⇒ e-y dy ex dx
On integrating
`int` e-y dy = `int` ex dx + C
⇒ -e-y = ex - C
∴ ex + e-y = C
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