y^{''}+(y^')2+9=0

Lösung

y^{^{''}} + (y^{^{'}}) 2 + 9 = 0

y = c_{1} + c_{2} e^{- 2 t} - \frac{9 t}{2}

Schritte zur Lösung

y^{''} (t) + (y^{'} (t)) 2 + 9 = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 t} - \frac{9 t}{2}

y = c_{1} + c_{2} e^{- 2 t} - \frac{9 t}{2}

y^{^{''}} - y^{^{'}} = t, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + y = tan (2 t)

y^{^{''}} + 5 y^{^{'}} + 6 y = sin (2 x)

y^{^{''}} - 4 y = e^{5 x}

y^{^{''}} + y^{^{'}} - 12 y = x e^{2 x}