5y^{''}+25y^'+1/(10^{-2)}y=10e^{-x/4}

Lösung

5 y^{^{''}} + 25 y^{^{'}} + \frac{1}{1 0 ^{- 2}} y = 10 e^{- \frac{x}{4}}

y = e^{- \frac{5 x}{2}} (c_{1} cos (\frac{5 5 ^{\frac{1}{2}} x}{2}) + c_{2} sin (\frac{5 5 ^{\frac{1}{2}} x}{2})) + \frac{32}{301} e^{- \frac{x}{4}}

Schritte zur Lösung

5 y^{''} (x) + 25 y^{'} (x) + \frac{1}{1 0 ^{- 2}} y = 10 e^{- \frac{x}{4}}

Solve linear ODE:

y = e^{- \frac{5 x}{2}} (c_{1} cos (\frac{5 5 ^{\frac{1}{2}} x}{2}) + c_{2} sin (\frac{5 5 ^{\frac{1}{2}} x}{2})) + \frac{32}{301} e^{- \frac{x}{4}}

y = e^{- \frac{5 x}{2}} (c_{1} cos (\frac{5 5 ^{\frac{1}{2}} x}{2}) + c_{2} sin (\frac{5 5 ^{\frac{1}{2}} x}{2})) + \frac{32}{301} e^{- \frac{x}{4}}

y^{^{''}} + 2 y^{^{'}} - 35 y = 13 sin (x) - e^{3 x} + 1

y^{^{''}} + a y^{^{'}} + y = e^{- 4 t}

y^{^{''}} + 9 y = 6 cos (3 x)

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

\frac{5}{6} q^{^{''}} + 10 q^{^{'}} + 60 q = 600