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If x² dy + 2xy = 2ln(x) , and y(1) = 0, then what is y(e)? dx x
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- e
- 1
- 1/e
- 1/e²
Correct Option: D
| x² y' + 2xy = | x |
| ⇒ y' + | y = | x | x3 |
| Comparing, we get P = | Q = | x' | x3 |

y(I.F.) = ∫ Q I.F. dx + c
| x² y = ∫ | . x²dx + C | x3 |
Solving above, find the value of C.
Putting x = 1, then find the value of y at x = e.
| Which is y = | e2 |