49y^{''}-168y^'+144y=0

Lösung

49 y^{^{''}} - 168 y^{^{'}} + 144 y = 0

y = c_{1} e^{\frac{12 t}{7}} + c_{2} e^{\frac{12 t}{7}} t

Schritte zur Lösung

49 y^{''} (t) - 168 y^{'} (t) + 144 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{12 t}{7}} + c_{2} e^{\frac{12 t}{7}} t

y = c_{1} e^{\frac{12 t}{7}} + c_{2} e^{\frac{12 t}{7}} t

(D^{3} - 8) y = 0

4 \frac{d ^{2} y}{d x ^{2}} + 36 y = 0

2 y - 3 y^{^{''}} = 0

y^{^{''}} + 4 y^{^{'}} - 7 y = 0

y^{^{'''}} - 5 y^{^{''}} + 17 y - 13 y = 0