y^{'''}-2y^{''}+5y^'=e^xcos(2x)

Lösung

y^{^{'''}} - 2 y^{^{''}} + 5 y^{^{'}} = e^{x} cos (2 x)

y = c_{1} + e^{x} (c_{2} cos (2 x) + c_{3} sin (2 x)) + \frac{e ^{x} x sin ( 2 x )}{20} - \frac{e ^{x} x cos ( 2 x )}{10}

Schritte zur Lösung

y^{'''} (x) - 2 y^{''} (x) + 5 y^{'} (x) = e^{x} cos (2 x)

Solve linear ODE:

y = c_{1} + e^{x} (c_{2} cos (2 x) + c_{3} sin (2 x)) + \frac{e ^{x} x sin ( 2 x )}{20} - \frac{e ^{x} x cos ( 2 x )}{10}

y = c_{1} + e^{x} (c_{2} cos (2 x) + c_{3} sin (2 x)) + \frac{e ^{x} x sin ( 2 x )}{20} - \frac{e ^{x} x cos ( 2 x )}{10}

(D^{2} - 3 D + 2) (D^{2} + 2 D + 1) y = x

y^{^{''}} - 60 y^{^{'}} - 900 y = 5 e^{10 x}

y^{^{''}} - 16 y = x e^{x}

\frac{d ^{2} y}{d x ^{2}} + c^{2} y = sec^{2} (c x)

y^{^{''}} - 3 y^{^{'}} + 5 y = 4 x^{3} - 2 x