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Question
Solve the following differential equation:
`("d"y)/("d"x) = "e"^(x + y) - x^3"e"^y`
Solution
`("d"y)/("d"x) "e"^(x + y) + x^3, ("e"^y)`
= ey[ex + x3]
`("d"y)/"e"^y` = dx(ex + x3)
The equation can be written as
`("d"y)/"e"^y` = (ex + x3)dx
Taking integration on both sides, we get
`int "e"^y "d"y = int ("e"^x + x^3) "d"x`
`"e"^y/(-1) = "e"^x + x^4/4 + "C"`
Where – C = C
Which is also constant
∴ `"e"^x + "e"^-y + x^4/4` = – C = C
∴ `"e"^x + "e"^-y + x^4/4` = C
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