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Beliebt Rechnen >

3y^{''}+12y^'-2y=0

Lösung

3 y^{^{''}} + 12 y^{^{'}} - 2 y = 0

Lösung

y = c_{1} e^{\frac{( - 6 + 42 ) t}{3}} + c_{2} e^{- \frac{( 6 + 42 ) t}{3}}

Schritte zur Lösung

3 y^{''} (t) + 12 y^{'} (t) - 2 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 6 + 42 ) t}{3}} + c_{2} e^{- \frac{( 6 + 42 ) t}{3}}

y = c_{1} e^{\frac{( - 6 + 42 ) t}{3}} + c_{2} e^{- \frac{( 6 + 42 ) t}{3}}

Graph

Beliebte Beispiele

y^{''}+200y^'+1000y=0

y^{^{''}} + 200 y^{^{'}} + 1000 y = 0

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

y^{''}+12y^'+32y=0

y^{^{''}} + 12 y^{^{'}} + 32 y = 0

(d^2x)/(dt^2)+53/49 (dx)/(dt)+49x=0

\frac{d ^{2} x}{d t ^{2}} + \frac{53}{49} \frac{d x}{d t} + 49 x = 0

y^{''}+18y^'+117y=0,y(0)=6,y^'(0)=3

y^{^{''}} + 18 y^{^{'}} + 117 y = 0, y (0) = 6, y^{^{'}} (0) = 3