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Beliebt Rechnen >

y^{''}-y=t,y(0)=1,y^'(0)=1

Lösung

y^{^{''}} - y = t, y (0) = 1, y^{^{'}} (0) = 1

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{^{''}} - 2 y + 5 = 0

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

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

y^{''}+y-5=e^{2x}-3cos(3x)

y^{^{''}} + y - 5 = e^{2 x} - 3 cos (3 x)

y^{'''}-18y^{''}+864y=e^{12x}

y^{^{'''}} - 18 y^{^{''}} + 864 y = e^{12 x}

(D^{3} - D) y = x