y^{''}+y^'-8y=48t

Lösung

y^{^{''}} + y^{^{'}} - 8 y = 48 t

y = c_{1} e^{\frac{( - 1 + 33 ) t}{2}} + c_{2} e^{\frac{( - 1 - 33 ) t}{2}} - 6 t - \frac{3}{4}

Schritte zur Lösung

y^{''} (t) + y^{'} (t) - 8 y = 48 t

Solve linear ODE:

y = c_{1} e^{\frac{( - 1 + 33 ) t}{2}} + c_{2} e^{\frac{( - 1 - 33 ) t}{2}} - 6 t - \frac{3}{4}

y = c_{1} e^{\frac{( - 1 + 33 ) t}{2}} + c_{2} e^{\frac{( - 1 - 33 ) t}{2}} - 6 t - \frac{3}{4}

y^{^{''}} - 2 y^{^{'}} + 1 = x e^{x}

y^{^{''}} + y^{^{'}} - 6 y = 6 e^{2 x}

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{x} - 9 + 24 x + 4

y^{^{''''}} - 2 y^{^{''}} + 1 = 0

x^{^{''}} + b \cdot x^{^{'}} + a = 0