Hallo,
1) y1'' = -7y1 +y2
2) y2'' = y1 -7y2
-------------------
2') y2'' = y1 -7y2
y1=y2'' +7y2
y1'=y2''' +7y2'
y1''=y2'''' +7y2'' ->Einsetzen in 1)
----->
y2'''' +7y2'' = -7y1 +y2
y2'''' +7y2'' = -7(y2'' +7y2) +y2
y2'''' +7y2'' = -7y2'' -49 y2 +y2
y2'''' +14y2'' +48 y2 =0
->Charakt, Gleichung :
k^4 +14 k^2 +48=0
(k^2+6)(k^2+8)=0
k1.2= ± 2i √2
k3.4= ± i √6
-->
y2=C1 cos(2√2 x) +C2 sin(2√2 x) +C3 cos(√6 x) +C4 sin(√6 x)
y1=y2'' +7y2