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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) - y = 0

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+y^'=0,y(pi/3)=16,y^'(pi/3)=-32

y^{^{''}} + y^{^{'}} = 0, y (\frac{π}{3}) = 16, y^{^{'}} (\frac{π}{3}) = - 32

(10d^3+d^2-7d+2)y=0

(10 d^{3} + d^{2} - 7 d + 2) y = 0

linear y^{'''}+3y^{''}-8y^'-30y=0

l in e a r y^{^{'''}} + 3 y^{^{''}} - 8 y^{^{'}} - 30 y = 0

y^{'''}-7y^{''}-8y^'+16y=0

y^{^{'''}} - 7 y^{^{''}} - 8 y^{^{'}} + 16 y = 0

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