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Beliebt Rechnen >

linear x^{''}+2x^'+10x=0

Lösung

linear

x^{^{''}} + 2 x^{^{'}} + 10 x = 0

Lösung

x = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t))

Schritte zur Lösung

x^{''} (t) + 2 x^{'} (t) + 10 x = 0

Solve linear ODE:

x = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t))

x = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t))

Graph

Beliebte Beispiele

f^{''}(t)-4f^'(t)+3f(t)=0,f(0)=3,f^'(0)=5

f^{^{''}} (t) - 4 f^{^{'}} (t) + 3 f (t) = 0, f (0) = 3, f^{^{'}} (0) = 5

1/8 y^{''}-2y=0

\frac{1}{8} y^{^{''}} - 2 y = 0

y^{''}-8y+20y=0

y^{^{''}} - 8 y + 20 y = 0

(D^4+6D^3+9D^2)y=0

(D^{4} + 6 D^{3} + 9 D^{2}) y = 0

(d^2y)/(dt^2)-6(dy)/(dt)+13y=0

\frac{d ^{2} y}{d t ^{2}} - 6 \frac{d y}{d t} + 13 y = 0