y^{''}-12y^'+36y=e^{6t}arctan(t)

Lösung

y^{^{''}} - 12 y^{^{'}} + 36 y = e^{6 t} arctan (t)

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{e ^{6 t} t ^{2} arctan ( t ) + e ^{6 t} t - e ^{6 t} t ln ( t ^{2} + 1 ) - e ^{6 t} arctan ( t )}{2}

Schritte zur Lösung

y^{''} (t) - 12 y^{'} (t) + 36 y = e^{6 t} arctan (t)

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{e ^{6 t} t ^{2} arctan ( t ) + e ^{6 t} t - e ^{6 t} t ln ( t ^{2} + 1 ) - e ^{6 t} arctan ( t )}{2}

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{e ^{6 t} t ^{2} arctan ( t ) + e ^{6 t} t - e ^{6 t} t ln ( t ^{2} + 1 ) - e ^{6 t} arctan ( t )}{2}

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{2 x}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y (0) = 0, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d x ^{2}} + 4 y = x - sin (3 x)

y^{^{''}} - 3 y^{^{'}} + 2 y = x cos (2 x)