81y^{''}-234y^'+169y=0

Lösung

81 y^{^{''}} - 234 y^{^{'}} + 169 y = 0

y = c_{1} e^{\frac{13 t}{9}} + c_{2} e^{\frac{13 t}{9}} t

Schritte zur Lösung

81 y^{''} (t) - 234 y^{'} (t) + 169 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{13 t}{9}} + c_{2} e^{\frac{13 t}{9}} t

y = c_{1} e^{\frac{13 t}{9}} + c_{2} e^{\frac{13 t}{9}} t

(d^{2} + 4 d + 4) y = 0

y^{^{'''}} - 15 y^{^{''}} + 66 y^{^{'}} - 80 y = 0

y^{^{''}} + k^{2} y^{^{'}} = 0

(d^{2} + 1)^{2} y = 0

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