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Beliebt Rechnen >

y^{''}-5y^'+6y=t,y(0)=0,y^'(0)=1

Lösung

y^{^{''}} - 5 y^{^{'}} + 6 y = t, y (0) = 0, y^{^{'}} (0) = 1

Lösung

y = (\frac{5}{4} - \frac{5}{36}) e^{3 t} - \frac{5}{4} e^{2 t} + \frac{t}{6} + \frac{5}{36}

Schritte zur Lösung

y^{''} (t) - 5 y^{'} (t) + 6 y = t

Solve linear ODE:

y = (\frac{5}{4} - \frac{5}{36}) e^{3 t} - \frac{5}{4} e^{2 t} + \frac{t}{6} + \frac{5}{36}

y = (\frac{5}{4} - \frac{5}{36}) e^{3 t} - \frac{5}{4} e^{2 t} + \frac{t}{6} + \frac{5}{36}

Graph

Beliebte Beispiele

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

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

y^{''}-y^'=1,y(0)=18,y^'(0)=1

y^{^{''}} - y^{^{'}} = 1, y (0) = 18, y^{^{'}} (0) = 1

y^{^{''}} + 5 y = (x)

x^{''}-16x^'+64x=5te^{8t}

x^{^{''}} - 16 x^{^{'}} + 64 x = 5 t e^{8 t}

y^{''}-5y^'+6y=-2x+1

y^{^{''}} - 5 y^{^{'}} + 6 y = - 2 x + 1