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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{\frac{( - 9 + 71 ) t}{2}} + c_{2} e^{\frac{( - 9 - 71 ) t}{2}}

Schritte zur Lösung

(2000) y^{''} (t) + 18000 y^{'} (t) + 5000 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 9 + 71 ) t}{2}} + c_{2} e^{\frac{( - 9 - 71 ) t}{2}}

y = c_{1} e^{\frac{( - 9 + 71 ) t}{2}} + c_{2} e^{\frac{( - 9 - 71 ) t}{2}}

Graph

Beliebte Beispiele

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

25y+8y^'+y^{''}=0

25 y + 8 y^{^{'}} + y^{^{''}} = 0

4/32 y^{''}+3y^'=0

\frac{4}{32} y^{^{''}} + 3 y^{^{'}} = 0