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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} - t^{2} + \frac{t}{3} - \frac{7}{18}

Schritte zur Lösung

y^{''} (t) - y^{'} (t) - 6 y = 6 t^{2}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} - t^{2} + \frac{t}{3} - \frac{7}{18}

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} - t^{2} + \frac{t}{3} - \frac{7}{18}

Graph

Beliebte Beispiele

y^{''}-3y^'=4sin(x)

y^{^{''}} - 3 y^{^{'}} = 4 sin (x)

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

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

y^{''}-2y^'-3y=6xe^{3x}

y^{^{''}} - 2 y^{^{'}} - 3 y = 6 x e^{3 x}

y^{''}+4y^'+3y=e^{5x}

y^{^{''}} + 4 y^{^{'}} + 3 y = e^{5 x}

y^{'''}-6y^{''}+11y^'-6y+x^2=-1

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y + x^{2} = - 1