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Beliebt Rechnen >

y^{''}-4y^'-21y=0,y(0)=a,y^'(0)=24

Lösung

y^{^{''}} - 4 y^{^{'}} - 21 y = 0, y (0) = a, y^{^{'}} (0) = 24

Lösung

y = e^{7 t} (a + \frac{24 - 7 a}{10}) - \frac{e ^{- 3 t} ( 24 - 7 a )}{10}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) - 21 y = 0

Solve linear ODE:

y = e^{7 t} (a + \frac{24 - 7 a}{10}) - \frac{e ^{- 3 t} ( 24 - 7 a )}{10}

y = e^{7 t} (a + \frac{24 - 7 a}{10}) - \frac{e ^{- 3 t} ( 24 - 7 a )}{10}

Graph

Beliebte Beispiele

y^{''}-3y^'+2y=0,y(0)=0,y^'(0)=6

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 6

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

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

y^{''}-y^'-120y=0

y^{^{''}} - y^{^{'}} - 120 y = 0

c \cdot y^{^{''}} + y^{^{'}} = 0

(d^2y)/(dx^2)-12(dy)/(dx)+52y=0

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 52 y = 0