81y^{''}-36y^'+8y=0

Lösung

81 y^{^{''}} - 36 y^{^{'}} + 8 y = 0

y = e^{\frac{2 t}{9}} (c_{1} cos (\frac{2 t}{9}) + c_{2} sin (\frac{2 t}{9}))

Schritte zur Lösung

81 y^{''} (t) - 36 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = e^{\frac{2 t}{9}} (c_{1} cos (\frac{2 t}{9}) + c_{2} sin (\frac{2 t}{9}))

y = e^{\frac{2 t}{9}} (c_{1} cos (\frac{2 t}{9}) + c_{2} sin (\frac{2 t}{9}))

\frac{d ^{2} y}{d t ^{2}} + 3 \frac{d y}{d t} - 10 y = 0

y^{^{''}} + 10 y^{^{'}} + 34 y = 0, y (0) = 1, y^{^{'}} (0) = 2

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

x^{^{''}} - 26 x^{^{'}} + 25 x = 0, x (0) = - 1, x^{^{'}} (0) = 2

D^{2} (D + 4)^{3} y = 0