y^{'''}-7y^'-6y=sin(2x)-5

Lösung

y^{^{'''}} - 7 y^{^{'}} - 6 y = sin (2 x) - 5

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} + \frac{5}{6} + \frac{- 3 sin ( 2 x ) + 11 cos ( 2 x )}{260}

Schritte zur Lösung

y^{'''} (x) - 7 y^{'} (x) - 6 y = sin (2 x) - 5

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} + \frac{5}{6} + \frac{- 3 sin ( 2 x ) + 11 cos ( 2 x )}{260}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} + \frac{5}{6} + \frac{- 3 sin ( 2 x ) + 11 cos ( 2 x )}{260}

2 y^{^{''}} - y^{^{'}} - 6 y = - 7 e^{2 x}, y (0) = 5, y^{^{'}} (0) = 2

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

y^{^{''}} + 3 y^{^{'}} - 10 = 0, y (0) = 0, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} + \frac{d}{d x} (8 y) + 65 y = 100

y^{^{''}} + 2 y^{^{'}} - 15 y = - 5 x^{2} + 3 x - 3