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Beliebt Rechnen >

45x^{''}+120x^'+15x=0

Lösung

45 x^{^{''}} + 120 x^{^{'}} + 15 x = 0

Lösung

x = c_{1} e^{\frac{( - 4 + 13 ) t}{3}} + c_{2} e^{- \frac{( 4 + 13 ) t}{3}}

Schritte zur Lösung

45 x^{''} (t) + 120 x^{'} (t) + 15 x = 0

Solve linear ODE:

x = c_{1} e^{\frac{( - 4 + 13 ) t}{3}} + c_{2} e^{- \frac{( 4 + 13 ) t}{3}}

x = c_{1} e^{\frac{( - 4 + 13 ) t}{3}} + c_{2} e^{- \frac{( 4 + 13 ) t}{3}}

Graph

Beliebte Beispiele

y^{''}+y^'-6y=0,y(0)=-2,y^'(0)=16

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = - 2, y^{^{'}} (0) = 16

v^{''}+v^'*1000+v*125000=0

v^{^{''}} + v^{^{'}} \cdot 1000 + v \cdot 125000 = 0

y^{''}+40y^'+490y=0

y^{^{''}} + 40 y^{^{'}} + 490 y = 0

y^{''}-9y=0,y(0)=3,y^'(0)=-9

y^{^{''}} - 9 y = 0, y (0) = 3, y^{^{'}} (0) = - 9

y^{''}-25y^'+144y=0,y^'(0)=5

y^{^{''}} - 25 y^{^{'}} + 144 y = 0, y^{^{'}} (0) = 5