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

Lösung

y^{^{''}} - 2 \cdot y^{^{'}} + y = 0

y = c_{1} e^{t} + c_{2} t e^{t}

Schritte zur Lösung

y^{''} (t) - 2 \cdot y^{'} (t) + y = 0

Solve linear ODE:

y = c_{1} e^{t} + c_{2} t e^{t}

y = c_{1} e^{t} + c_{2} t e^{t}

25 y^{^{''}} + 40 y^{^{'}} + 16 y = 0

y^{^{''}} + 3 y^{^{'}} - 10 y = 0, y (0) = 2, y^{^{'}} (0) = 4

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = 0, y^{^{'}} (0) = 6

y^{^{''}} + 14 y^{^{'}} + 48 y = 0, y (0) = 9, y^{^{'}} (0) = - 66

y^{^{''''}} = 625 y