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प्रश्न
Solve the differential equation `"dy"/"dx" + 2xy` = y
उत्तर
Given equation is `"dy"/"dx" + 2xy` = y.
⇒ `"dy"/"dx"` = y – xy
⇒ `"dy"/"dx"` = y(1 –2x)
⇒ `"dy"/y` = (1 –2x)dx
Integrating both sides, we have
`int "dy"/"dx" = int (1 - 2x)"d"x`
⇒ log y = x – x2 + log c
⇒ log y – log c = x – x2
⇒ `log y/"c"` = x – x2
⇒ `y/"c" = "e"^(x - x^2)`
∴ y = `"c" . "e"^(x - x^2)`
Hence, the required solution is y = `"c" . "e"^(x - x^2)` .
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