y^{''}+5/6 y^'+2/15 y= 4/3

Lösung

y^{^{''}} + \frac{5}{6} y^{^{'}} + \frac{2}{15} y = \frac{4}{3}

y = c_{1} e^{\frac{( - 25 + 145 ) t}{60}} + c_{2} e^{\frac{( - 25 - 145 ) t}{60}} + 10

Schritte zur Lösung

y^{''} (t) + \frac{5}{6} y^{'} (t) + \frac{2}{15} y = \frac{4}{3}

Solve linear ODE:

y = c_{1} e^{\frac{( - 25 + 145 ) t}{60}} + c_{2} e^{\frac{( - 25 - 145 ) t}{60}} + 10

y = c_{1} e^{\frac{( - 25 + 145 ) t}{60}} + c_{2} e^{\frac{( - 25 - 145 ) t}{60}} + 10

y^{^{''}} - y = x + sin (x), y (0) = 2, y^{^{'}} (0) = 3

y^{^{''}} - 5 y^{^{'}} + 6 y = 20 sin (8 x)

y^{^{''}} + 2 y^{^{'}} + y = cos (x)

y^{^{''}} + 4 y = g (t), y (0) = 0, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 6 y = 3 x^{2} - 8