y^{''}-8y^'+16y=e^{4t}ln(t)

Lösung

y^{^{''}} - 8 y^{^{'}} + 16 y = e^{4 t} ln (t)

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{2 e ^{4 t} t ^{2} ln ( t ) - 3 e ^{4 t} t ^{2}}{4}

Schritte zur Lösung

y^{''} (t) - 8 y^{'} (t) + 16 y = e^{4 t} ln (t)

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{2 e ^{4 t} t ^{2} ln ( t ) - 3 e ^{4 t} t ^{2}}{4}

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{2 e ^{4 t} t ^{2} ln ( t ) - 3 e ^{4 t} t ^{2}}{4}

10 y^{^{''}} + 1000 y = 100 cos (8 t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y^{^{'}} + 14 y = 2 + t, y (0) = 1, y^{^{'}} (0) = 1

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 9 e^{- t} + 3

y^{^{''}} + 10 y^{^{'}} + 25 y = 14 \cdot e^{- 5 x}

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 9 e^{- t} + 6