-4y^{''}+9y=15

Lösung

- 4 y^{^{''}} + 9 y = 15

y = c_{1} e^{\frac{3 t}{2}} + c_{2} e^{- \frac{3 t}{2}} + \frac{5}{3}

Schritte zur Lösung

- 4 y^{''} (t) + 9 y = 15

Solve linear ODE:

y = c_{1} e^{\frac{3 t}{2}} + c_{2} e^{- \frac{3 t}{2}} + \frac{5}{3}

y = c_{1} e^{\frac{3 t}{2}} + c_{2} e^{- \frac{3 t}{2}} + \frac{5}{3}

y^{^{''}} - y = x^{2} e^{x} + e^{3 x}

y^{^{''}} + 6 y^{^{'}} + 13 y = 10 e^{- 2 t}

y^{^{''}} + y = t + t sin (t)

y^{^{''}} - 9 y^{^{'}} = 81 x^{2} + 7

y^{^{''}} + y = sec^{3} (x), y (0) = 1