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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{- t} (2 cos (2 t) - \frac{1}{2} sin (2 t))

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + 3 y = 0

Solve linear ODE:

y = e^{- t} (2 cos (2 t) - \frac{1}{2} sin (2 t))

y = e^{- t} (2 cos (2 t) - \frac{1}{2} sin (2 t))

Graph

Beliebte Beispiele

y^{'''}-y^{''}-46y^'-80y=0

y^{^{'''}} - y^{^{''}} - 46 y^{^{'}} - 80 y = 0

3y^{''}+11y^'-4y=0,y(0)=4,y^'(0)=10

3 y^{^{''}} + 11 y^{^{'}} - 4 y = 0, y (0) = 4, y^{^{'}} (0) = 10

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

l in e a r y^{^{''''}} - 2 y^{^{''}} + y = 0

y^{'''}-5y^{''}+8y^'-4y=0

y^{^{'''}} - 5 y^{^{''}} + 8 y^{^{'}} - 4 y = 0

y^{''}-2y^'+y=0,y(1)=3,y^'(1)=2

y^{^{''}} - 2 y^{^{'}} + y = 0, y (1) = 3, y^{^{'}} (1) = 2