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Beliebt Rechnen >

y^{''}-3y^'-4y=0,y(0)=a,y^'(0)=-15

Lösung

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = a, y^{^{'}} (0) = - 15

Lösung

y = e^{4 t} (a + \frac{- 15 - 4 a}{5}) - \frac{e ^{- t} ( - 15 - 4 a )}{5}

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) - 4 y = 0

Solve linear ODE:

y = e^{4 t} (a + \frac{- 15 - 4 a}{5}) - \frac{e ^{- t} ( - 15 - 4 a )}{5}

y = e^{4 t} (a + \frac{- 15 - 4 a}{5}) - \frac{e ^{- t} ( - 15 - 4 a )}{5}

Graph

Beliebte Beispiele

y^{''''}-y^{'''}-y^{''}-y^'-2y=0

y^{^{''''}} - y^{^{'''}} - y^{^{''}} - y^{^{'}} - 2 y = 0

4y^{''''}+8y^{''}+4y=0

4 y^{^{''''}} + 8 y^{^{''}} + 4 y = 0

(D^2+2)^3(D^2-3)^2y=0

(D^{2} + 2)^{3} (D^{2} - 3)^{2} y = 0

(D^{2} + 1)^{3} y = 0

y^{''}-y^'-12y=0,y(0)=1,y^'(0)=-2

y^{^{''}} - y^{^{'}} - 12 y = 0, y (0) = 1, y^{^{'}} (0) = - 2