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

Lösung

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

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{10} sin (x) + \frac{1}{5} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{10} sin (x) + \frac{1}{5} cos (x)

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{10} sin (x) + \frac{1}{5} cos (x)

so l v e f or d, d (t) = 4000 - 3000 e^{- 0.06 t}

(d^{2} - d - 2) \cdot y = 2 \cdot lo g_{10} (x) + \frac{1}{x} + \frac{1}{( x ^{2} )}

(d - 5)^{2} y = e^{5 x}

(d^{2} - 5 d + 6) \cdot y = x

y^{^{''}} - 6 y^{^{'}} + 8 y = 16 x^{2} - 2