Re: 一題高階非線性問題

[Honor1984 (奈何上天造化弄人？)]

※ 引述《nini851216 (解壓縮)》之銘言：
: https://i.imgur.com/nB6oRph.jpg
: 字太醜見諒
: 再來就不會了..
: 請求大大幫忙
: https://i.imgur.com/BDv93Cp.jpg
: 答案是這個
: https://i.imgur.com/L3KLflc.jpg

yy" + (y')^2 = 2

=> y"/y' + y'/y = 2/(yy')

=> [lny']' + [lny]' = 2/(yy')

=> [ln(yy')]' = 2/(yy')

=> yy' = 2x + C_1

=> (1/2) (y^2)' = 2x + C_1

=> (1/2)y^2 = x^2 + C_1x  寫成這樣就可以了

=> y^2 = 2{[x + C_2]^2 - (C_2)^2}

=> x + C_2 = +-(1/2)sqrt(2y^2 + C_3)

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推 nini851216  : 謝謝你 我會了！