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Beliebt Rechnen >

5f^{''}(t)+50f^'(t)+f(t)=0

Lösung

5 f^{^{''}} (t) + 50 f^{^{'}} (t) + f (t) = 0

Lösung

f (t) = c_{1} e^{\frac{( - 25 + 2 155 ) t}{5}} + c_{2} e^{- \frac{( 25 + 2 155 ) t}{5}}

Schritte zur Lösung

5 f^{''} (t) + 50 f^{'} (t) + f (t) = 0

Solve linear ODE:

f (t) = c_{1} e^{\frac{( - 25 + 2 155 ) t}{5}} + c_{2} e^{- \frac{( 25 + 2 155 ) t}{5}}

f (t) = c_{1} e^{\frac{( - 25 + 2 155 ) t}{5}} + c_{2} e^{- \frac{( 25 + 2 155 ) t}{5}}

Graph

Beliebte Beispiele

(d^2y)/(dx^2)=-6y

\frac{d ^{2} y}{d x ^{2}} = - 6 y

(2000)y^{''}+18000y^'+5000y=0

(2000) y^{^{''}} + 18000 y^{^{'}} + 5000 y = 0

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

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

(D^2+2)3(D^2-3)2y=0

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

y^{''}-6y^'+9y=0,y(0)=5,y^'(0)=12

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 5, y^{^{'}} (0) = 12