3y^{''}-5y^'-12y=0

Lösung

3 y^{^{''}} - 5 y^{^{'}} - 12 y = 0

y = c_{1} e^{3 t} + c_{2} e^{- \frac{4 t}{3}}

Schritte zur Lösung

3 y^{''} (t) - 5 y^{'} (t) - 12 y = 0

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- \frac{4 t}{3}}

y = c_{1} e^{3 t} + c_{2} e^{- \frac{4 t}{3}}

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

y^{^{''}} + cy = 0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 13 y = 0

y^{^{''}} - y^{^{'}} - 20 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 12 y^{^{'}} + 35 y = 0, y (0) = 1, y^{^{'}} (0) = - 1