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Beliebt Rechnen >

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

Lösung

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

Lösung

y = (\frac{1}{10} + \frac{2}{5}) e^{t} - \frac{1}{10} e^{- t} - \frac{1}{5} e^{t} sin (t) - \frac{2}{5} e^{t} cos (t)

Schritte zur Lösung

y^{''} (t) - y = e^{t} sin (t)

Solve linear ODE:

y = (\frac{1}{10} + \frac{2}{5}) e^{t} - \frac{1}{10} e^{- t} - \frac{1}{5} e^{t} sin (t) - \frac{2}{5} e^{t} cos (t)

y = (\frac{1}{10} + \frac{2}{5}) e^{t} - \frac{1}{10} e^{- t} - \frac{1}{5} e^{t} sin (t) - \frac{2}{5} e^{t} cos (t)

Graph

Beliebte Beispiele

y^{''}-2y^'+2y=4e^xcos(x)

y^{^{''}} - 2 y^{^{'}} + 2 y = 4 e^{x} cos (x)

y^{''}+2y^'-5y=-2

y^{^{''}} + 2 y^{^{'}} - 5 y = - 2

4y^{''}+16y=1,y(0)=-2,y^'(0)=0

4 y^{^{''}} + 16 y = 1, y (0) = - 2, y^{^{'}} (0) = 0

y^{^{''}} + y = t^{3}

y^{''}-8y^'+16y=x

y^{^{''}} - 8 y^{^{'}} + 16 y = x