25y^{''}-90y^'+81y=0

Lösung

25 y^{^{''}} - 90 y^{^{'}} + 81 y = 0

y = c_{1} e^{\frac{9 t}{5}} + c_{2} e^{\frac{9 t}{5}} t

Schritte zur Lösung

25 y^{''} (t) - 90 y^{'} (t) + 81 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{9 t}{5}} + c_{2} e^{\frac{9 t}{5}} t

y = c_{1} e^{\frac{9 t}{5}} + c_{2} e^{\frac{9 t}{5}} t

- x^{^{''}} + a x = 0

y^{^{''''}} - a y = 0

x^{^{''}} + 2 x^{^{'}} + 8 x = 0

y^{^{'''}} - y^{^{''}} + 9 y^{^{'}} - 9 y = 0

y^{^{''}} - 12 y^{^{'}} + 136 y = 0