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Beliebt Rechnen >

y^{''}+0.5y^'+y=0

Lösung

y^{^{''}} + 0.5 y^{^{'}} + y = 0

Lösung

y = e^{- \frac{t}{4}} (c_{1} cos (\frac{15 t}{4}) + c_{2} sin (\frac{15 t}{4}))

Schritte zur Lösung

y^{''} (t) + 0.5 y^{'} (t) + y = 0

Solve linear ODE:

y = e^{- \frac{t}{4}} (c_{1} cos (\frac{15 t}{4}) + c_{2} sin (\frac{15 t}{4}))

y = e^{- \frac{t}{4}} (c_{1} cos (\frac{15 t}{4}) + c_{2} sin (\frac{15 t}{4}))

Graph

Beliebte Beispiele

y^{''}+8y^'+20y=0,y(0)=1,y^'(0)=7

y^{^{''}} + 8 y^{^{'}} + 20 y = 0, y (0) = 1, y^{^{'}} (0) = 7

x^{''}-x^'-110x=0,x(0)=14

x^{^{''}} - x^{^{'}} - 110 x = 0, x (0) = 14

3y^{''}+5y^'+y=0

3 y^{^{''}} + 5 y^{^{'}} + y = 0

y^{''}+16y=0,y(0)=3,y^'(0)=1

y^{^{''}} + 16 y = 0, y (0) = 3, y^{^{'}} (0) = 1

y^{''}+16y=0,y(0)=3,y^'(0)=0

y^{^{''}} + 16 y = 0, y (0) = 3, y^{^{'}} (0) = 0