y^{''}-5/2 y^'+y=0

Lösung

y^{^{''}} - \frac{5}{2} y^{^{'}} + y = 0

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

Schritte zur Lösung

y^{''} (t) - \frac{5}{2} y^{'} (t) + y = 0

Solve linear ODE:

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

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

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

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = 1

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

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = 2

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 25 y = 0