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Beliebt Rechnen >

2y^{''}+6y^'+8y=0,y(0)=5,y^'(0)=0

Lösung

2 y^{^{''}} + 6 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

Lösung

y = e^{- \frac{3 t}{2}} (5 cos (\frac{7 t}{2}) + \frac{15}{7} sin (\frac{7 t}{2}))

Schritte zur Lösung

2 y^{''} (t) + 6 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = e^{- \frac{3 t}{2}} (5 cos (\frac{7 t}{2}) + \frac{15}{7} sin (\frac{7 t}{2}))

y = e^{- \frac{3 t}{2}} (5 cos (\frac{7 t}{2}) + \frac{15}{7} sin (\frac{7 t}{2}))

Graph

Beliebte Beispiele

y^{''}+y^'-20y=0,y(0)=1,y(0)=22

y^{^{''}} + y^{^{'}} - 20 y = 0, y (0) = 1, y (0) = 22

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

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

(d^2y)/(dx^2)-5(dy)/(dx)=0

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} = 0

y^{''}+6y^'+10y=0,y(0)=4

y^{^{''}} + 6 y^{^{'}} + 10 y = 0, y (0) = 4

6y^{''}+5y^'-6y=0

6 y^{^{''}} + 5 y^{^{'}} - 6 y = 0