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Beliebt Rechnen >

2y^{''}-2y^'+y=0,y(0)=-1,y^'(0)=0

Lösung

2 y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = - 1, y^{^{'}} (0) = 0

Lösung

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

Schritte zur Lösung

2 y^{''} (t) - 2 y^{'} (t) + y = 0

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+4y=0,y(pi)=0,y(0)=0

y^{^{''}} + 4 y = 0, y (π) = 0, y (0) = 0

y^{''}+2y^'-8y=0,y^'(0)=14

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y^{^{'}} (0) = 14

9y^{''}+4y^'+5y=0,y(0)=2,y^'(0)=0

9 y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = 0

4 y^{^{''}} - 36 y = 0

100y^{''}+60y^'+90y=0,y(1)=9,y^'(1)=2

100 y^{^{''}} + 60 y^{^{'}} + 90 y = 0, y (1) = 9, y^{^{'}} (1) = 2