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Beliebt Rechnen >

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

Lösung

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

Lösung

y = 2 c_{2} e^{\frac{t}{2}} + c_{2} e^{- t} - 1

Schritte zur Lösung

2 y^{''} (t) + y^{'} (t) - y = 1

Solve linear ODE:

y = 2 c_{2} e^{\frac{t}{2}} + c_{2} e^{- t} - 1

y = 2 c_{2} e^{\frac{t}{2}} + c_{2} e^{- t} - 1

Graph

Beliebte Beispiele

y^{''}-3y^'+2y=e^3x

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{3} x

2y^{''}-y^'-y=3e^x+2e^{-x}

2 y^{^{''}} - y^{^{'}} - y = 3 e^{x} + 2 e^{- x}

y^{''}+2y^'+y=t^{(-1)}e^{(-t)}

y^{^{''}} + 2 y^{^{'}} + y = t^{(- 1)} e^{(- t)}

y^{''}-y^'-6y=2e^{3t},y(0)=3,y^'(0)=1

y^{^{''}} - y^{^{'}} - 6 y = 2 e^{3 t}, y (0) = 3, y^{^{'}} (0) = 1

y^{^{''}} + 6 y^{^{'}} = 5 x