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Beliebt Rechnen >

y^{''}+4y^'+7y=0,y(0)=3,y^'(0)=7

Lösung

y^{^{''}} + 4 y^{^{'}} + 7 y = 0, y (0) = 3, y^{^{'}} (0) = 7

Lösung

y = e^{- 2 t} (3 cos (3 t) + \frac{13}{3} sin (3 t))

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 7 y = 0

Solve linear ODE:

y = e^{- 2 t} (3 cos (3 t) + \frac{13}{3} sin (3 t))

y = e^{- 2 t} (3 cos (3 t) + \frac{13}{3} sin (3 t))

Graph

Beliebte Beispiele

2y^{''}-4y^'-5y=0

2 y^{^{''}} - 4 y^{^{'}} - 5 y = 0

y^{''''}+2y^{'''}-5y^{''}-5y^'+1/2 y=0

y^{^{''''}} + 2 y^{^{'''}} - 5 y^{^{''}} - 5 y^{^{'}} + \frac{1}{2} y = 0

y^{'''}-7y^{''}+10y^'=0

y^{^{'''}} - 7 y^{^{''}} + 10 y^{^{'}} = 0

y^{'''}+6y^{''}-16y^'=0

y^{^{'''}} + 6 y^{^{''}} - 16 y^{^{'}} = 0

625x^{''}+100x^'+3x=0,x(0)=25,x^'(0)=-2

625 x^{^{''}} + 100 x^{^{'}} + 3 x = 0, x (0) = 25, x^{^{'}} (0) = - 2