y^{'''}-2y^'+4y=e^xcos(x)+x^2

Lösung

y^{^{'''}} - 2 y^{^{'}} + 4 y = e^{x} cos (x) + x^{2}

y = c_{1} e^{- 2 x} + e^{x} (c_{2} cos (x) + c_{3} sin (x)) + \frac{3 e ^{x} x sin ( x ) - e ^{x} x cos ( x )}{20} + \frac{x ^{2} + x}{4} + \frac{1}{8}

Schritte zur Lösung

y^{'''} (x) - 2 y^{'} (x) + 4 y = e^{x} cos (x) + x^{2}

Solve linear ODE:

y = c_{1} e^{- 2 x} + e^{x} (c_{2} cos (x) + c_{3} sin (x)) + \frac{3 e ^{x} x sin ( x ) - e ^{x} x cos ( x )}{20} + \frac{x ^{2} + x}{4} + \frac{1}{8}

y = c_{1} e^{- 2 x} + e^{x} (c_{2} cos (x) + c_{3} sin (x)) + \frac{3 e ^{x} x sin ( x ) - e ^{x} x cos ( x )}{20} + \frac{x ^{2} + x}{4} + \frac{1}{8}

y^{^{''}} + 1000 y^{^{'}} + 2500 y = 30

y^{^{''}} - 3 y^{^{'}} - 9 y = 4 cos (2 x) - 5 e^{x}

2 y^{^{''}} - 5 y^{^{'}} - 3 y = 1 + 2 e^{t} + e^{2 t}

x^{^{''}} + 100 x^{^{'}} + 2470 = 0

x^{^{''}} - 9 x^{^{'}} - 14 = 0