y^{'''}-5y^{''}+6y^'=8+2sin(x)

Lösung

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 8 + 2 sin (x)

y = c_{1} + c_{2} e^{2 x} + c_{3} e^{3 x} + \frac{4 x}{3} + \frac{1}{5} sin (x) - \frac{1}{5} cos (x)

Schritte zur Lösung

y^{'''} (x) - 5 y^{''} (x) + 6 y^{'} (x) = 8 + 2 sin (x)

Solve linear ODE:

y = c_{1} + c_{2} e^{2 x} + c_{3} e^{3 x} + \frac{4 x}{3} + \frac{1}{5} sin (x) - \frac{1}{5} cos (x)

y = c_{1} + c_{2} e^{2 x} + c_{3} e^{3 x} + \frac{4 x}{3} + \frac{1}{5} sin (x) - \frac{1}{5} cos (x)

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

y^{^{''}} - 2 y^{^{'}} + y = \frac{11 e ^{t}}{1 + t ^{2}}

y^{^{'''}} - 4 y^{^{''}} + 6 y^{^{'}} - 4 y = x + e^{x} cos (x)

y^{^{''}} + 16 y = 9 sec (4 x)

y^{^{''}} - 3 y^{^{'}} + y = 8 x