y^{''}-y^'-6y=(x^2+3x)e^{2x}+cos(2x)

Lösung

y^{^{''}} - y^{^{'}} - 6 y = (x^{2} + 3 x) e^{2 x} + cos (2 x)

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} + \frac{- 104 e ^{2 x} x ^{2} - 468 e ^{2 x} x - 403 e ^{2 x} - 8 sin ( 2 x ) - 40 cos ( 2 x )}{416}

Schritte zur Lösung

y^{''} (x) - y^{'} (x) - 6 y = (x^{2} + 3 x) e^{2 x} + cos (2 x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} + \frac{- 104 e ^{2 x} x ^{2} - 468 e ^{2 x} x - 403 e ^{2 x} - 8 sin ( 2 x ) - 40 cos ( 2 x )}{416}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} + \frac{- 104 e ^{2 x} x ^{2} - 468 e ^{2 x} x - 403 e ^{2 x} - 8 sin ( 2 x ) - 40 cos ( 2 x )}{416}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 12 y = 20 cos (3 x)

y^{^{''}} + 6 y^{^{'}} + 13 y = e^{- 3 x} \cdot cos (2 x)

y^{^{''}} - y^{^{'}} + y = 6 sin (t) - 3 e^{2 t}

y^{^{''}} - 6 y^{^{'}} + 9 y = 18 x - 3

y^{^{''}} - 2 y^{^{'}} + 5 y = 4 e^{3 t}, y (0) = 0, y^{^{'}} (0) = - 3