Edo No Homogenea.docx
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π΄Γ©πππ
π ππππππππ
π πππππππππππ
π ππππππ
ππππ πβ²β² + ππβ² + ππ = π + π π· 2 + 2π· + 2 = 0 π·=
βπ Β± βπ 2 β 4ππ 2π
π·=
β2 Β± β(2)2 β 4(1)(2) 2(1)
π·=
β2 Β± β4 2
π·1 =
β2 + ββ4 = β1 + π 2
π·2 =
β2 + ββ4 = β1 β π 2
π πππππ πππππππππ πππππ’πππππ
ππ = πͺπ πβπ ππ¨π¬ π + πͺπ πβπ πππ π ππ π(π₯) = π(π₯) π(π₯) = 1 + π₯ ππ = π(π₯) β π(π·) π(π·) = ππ = (1 + π₯) β
π·2
1 πΉ(π·)
1 + 2π· + 2
1 β1 βπ· βπ· π·
1 β π·2 2 1 β π·2 2 +π·2 1 2 π· 2 1 β π·2 2
2 +2π· 1 1 β π· 2 2 1 + π·3 2 1 + π·3 2 1 + π·3 2
1 1 1 ππ = (1 + π₯) ( β π· + π· 2 ) 2 2 4 1 1 1 ππ = (1 + π₯) β π·(1 + π₯) + π· 2 (1 + π₯) 2 2 4
1 β π·4 4 1 β π·4 4
+π·2 1 + π·2 4
ππ =
1 π₯ 1 π 1 π (1 + π₯) + β (1 + π₯) + β β 2 2 2 ππ₯ 4 ππ₯
ππ =
1 π₯ 1 1 π (1) + β β (1) + β 2 2 2 4 ππ₯
ππ =
1 π₯ 1 1 + β β (1) + β (0) 2 2 2 4
1 π₯ 1 + β 2 2 2 π ππ = π ππ =
π = πβ + ππ π = πΆ1 π βπ₯ cos π₯ + πΆ2 π βπ₯ π ππ π₯ +
π₯ 2
π = πβπ (πͺπ ππ¨π¬ π + πͺπ πππ π) +
π π
βπ Β± βπ 2 β 4ππ 2π
π·=
β2 Β± β(2)2 β 4(1)(2) 2(1)
π·=
β2 Β± β4 2
π·1 =
β2 + ββ4 = β1 + π 2
π·2 =
β2 + ββ4 = β1 β π 2
π πππππ πππππππππ πππππ’πππππ
ππ = πͺπ πβπ ππ¨π¬ π + πͺπ πβπ πππ π ππ π(π₯) = π(π₯) π(π₯) = 1 + π₯ ππ = π(π₯) β π(π·) π(π·) = ππ = (1 + π₯) β
π·2
1 πΉ(π·)
1 + 2π· + 2
1 β1 βπ· βπ· π·
1 β π·2 2 1 β π·2 2 +π·2 1 2 π· 2 1 β π·2 2
2 +2π· 1 1 β π· 2 2 1 + π·3 2 1 + π·3 2 1 + π·3 2
1 1 1 ππ = (1 + π₯) ( β π· + π· 2 ) 2 2 4 1 1 1 ππ = (1 + π₯) β π·(1 + π₯) + π· 2 (1 + π₯) 2 2 4
1 β π·4 4 1 β π·4 4
+π·2 1 + π·2 4
ππ =
1 π₯ 1 π 1 π (1 + π₯) + β (1 + π₯) + β β 2 2 2 ππ₯ 4 ππ₯
ππ =
1 π₯ 1 1 π (1) + β β (1) + β 2 2 2 4 ππ₯
ππ =
1 π₯ 1 1 + β β (1) + β (0) 2 2 2 4
1 π₯ 1 + β 2 2 2 π ππ = π ππ =
π = πβ + ππ π = πΆ1 π βπ₯ cos π₯ + πΆ2 π βπ₯ π ππ π₯ +
π₯ 2
π = πβπ (πͺπ ππ¨π¬ π + πͺπ πππ π) +
π π
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