64y^{''}+112y^'+49y=0

Lösung

64 y^{^{''}} + 112 y^{^{'}} + 49 y = 0

y = c_{1} e^{- \frac{7 t}{8}} + c_{2} e^{- \frac{7 t}{8}} t

Schritte zur Lösung

64 y^{''} (t) + 112 y^{'} (t) + 49 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{7 t}{8}} + c_{2} e^{- \frac{7 t}{8}} t

y = c_{1} e^{- \frac{7 t}{8}} + c_{2} e^{- \frac{7 t}{8}} t

\frac{1}{16} x^{^{''}} + 2 x^{^{'}} + x = 0

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 6, y^{^{'}} (0) = 10

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

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = 3, y^{^{'}} (0) = 7

4 \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 3 y = 0