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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{- \frac{t}{2}} (cos (\frac{3 t}{2}) + \frac{1}{3} sin (\frac{3 t}{2}))

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- \frac{t}{2}} (cos (\frac{3 t}{2}) + \frac{1}{3} sin (\frac{3 t}{2}))

y = e^{- \frac{t}{2}} (cos (\frac{3 t}{2}) + \frac{1}{3} sin (\frac{3 t}{2}))

Graph

Beliebte Beispiele

y^{''}-4y^'+4y=0,y(0)=5,y^'(0)=3

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 5, y^{^{'}} (0) = 3

(D^4+4D^3+2D^2-8D-8)y=0

(D^{4} + 4 D^{3} + 2 D^{2} - 8 D - 8) y = 0

(d^2y)/(dx^2)-(dy)/(dx)-6y=0

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 6 y = 0

(D^4-D^3-3D^2+D+2)y=0

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

b y^{^{''}} + a y = 0