y^{''}+4y^'+5y=35e^{-4}x

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = 35 e^{- 4} x

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{7 x}{e ^{4}} - \frac{28}{5 e ^{4}}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 5 y = 35 e^{- 4} x

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{7 x}{e ^{4}} - \frac{28}{5 e ^{4}}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{7 x}{e ^{4}} - \frac{28}{5 e ^{4}}

y^{^{''}} + 9 y = sin^{2} (t)

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

(d^{3} + 3 d^{2} + 2 d) y = x^{2}

(d^{2} - 2 d + 1) \cdot y = x \cdot e^{x} \cdot cos (x)

d^{2} (d^{2} + 1) y = 1