answer Question #2 only, disregard the other items

answer Question #2 only, disregard the other items. Kindly show the complete solution. I will like/upvote your asnwer if its clear to understand and complete solution. you. Transcribed Image Text: Show all necessary condition.
Determine whether the given function is a solution to the differential
equation and find the particular solution when initial-value condition is
1. у %3D хе-2х; 4у +4y’ +у” %3D 0
2. y =- Inx; x²y” + xy’ – y = lnx
3. У(x) %3 х3 (с + Inx); ху’ — Зу 3D х3, У(1) %3D 8
4. y(x) = tan(x³3 + c);y’ = 3x²(y² + 1), y(0) = 1


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