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Beliebt Rechnen >

y^{''}-3y^'+αy=0,y(0)=1,y^'(0)=5

Lösung

y^{^{''}} - 3 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = 5

Lösung

y = e^{\frac{t ( 3 + 9 - 4 α )}{2}} (1 + \frac{- - 4 α + 9 + 7}{2 9 - 4 α}) - \frac{e ^{\frac{t ( 3 - 9 - 4 α )}{2}} ( - - 4 α + 9 + 7 )}{2 9 - 4 α}

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) + α y = 0

Solve linear ODE:

y = e^{\frac{t ( 3 + 9 - 4 α )}{2}} (1 + \frac{- - 4 α + 9 + 7}{2 9 - 4 α}) - \frac{e ^{\frac{t ( 3 - 9 - 4 α )}{2}} ( - - 4 α + 9 + 7 )}{2 9 - 4 α}

y = e^{\frac{t ( 3 + 9 - 4 α )}{2}} (1 + \frac{- - 4 α + 9 + 7}{2 9 - 4 α}) - \frac{e ^{\frac{t ( 3 - 9 - 4 α )}{2}} ( - - 4 α + 9 + 7 )}{2 9 - 4 α}

Graph

Beliebte Beispiele

6y^{''}+y^'-2y=0,y(1)=2,y^'(1)= 1/6

6 y^{^{''}} + y^{^{'}} - 2 y = 0, y (1) = 2, y^{^{'}} (1) = \frac{1}{6}

x^{''}-0.1x^'+1.0025x=0

x^{^{''}} - 0.1 x^{^{'}} + 1.0025 x = 0

y^{^{'''}} + 6 y = 0

y^{''}+120y^'+10000y=0

y^{^{''}} + 120 y^{^{'}} + 10000 y = 0

4 y^{^{''}} = - 25 y