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Beliebt Rechnen >

y^{''}+2y^'+2y=t^2,y(0)= 1/2 ,y^'(0)=0

Lösung

y^{^{''}} + 2 y^{^{'}} + 2 y = t^{2}, y (0) = \frac{1}{2}, y^{^{'}} (0) = 0

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{'''}+265y^'=tan(16x)

y^{^{'''}} + 265 y^{^{'}} = tan (16 x)

y^{''}-10y^'+9y=e^{2x}

y^{^{''}} - 10 y^{^{'}} + 9 y = e^{2 x}

y^{''}+y^'-6y=e^{2t}+t

y^{^{''}} + y^{^{'}} - 6 y = e^{2 t} + t

y^{'''}-3y^{''}-y^'+3y=1+e^x

y^{^{'''}} - 3 y^{^{''}} - y^{^{'}} + 3 y = 1 + e^{x}

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

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