y^{''}-2y^'+y=3sqrt(t+1)e^{-t}

Lösung

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

y = c_{1} e^{t} + c_{2} t e^{t} + e^{t} \cdot \int - \frac{3 t t + 1}{e ^{2 t}} d t + \frac{3 2 e ^{2}}{2} e^{t} t (- \frac{1}{2} e^{- 2 t - 2} 2 t + 2 + \frac{π}{4} erf (2 t + 2))

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{t} + c_{2} t e^{t} + e^{t} \cdot \int - \frac{3 t t + 1}{e ^{2 t}} d t + \frac{3 2 e ^{2}}{2} e^{t} t (- \frac{1}{2} e^{- 2 t - 2} 2 t + 2 + \frac{π}{4} erf (2 t + 2))

y = c_{1} e^{t} + c_{2} t e^{t} + e^{t} \cdot \int - \frac{3 t t + 1}{e ^{2 t}} d t + \frac{3 2 e ^{2}}{2} e^{t} t (- \frac{1}{2} e^{- 2 t - 2} 2 t + 2 + \frac{π}{4} erf (2 t + 2))

2 y^{^{''}} + 14 y^{^{'}} + 12 y = 0.7

0.25 y^{^{''}} + 10 y^{^{'}} + 1000 = 0

y^{^{''}} - 12 y^{^{'}} + 36 y = 280 sin (x) - 184 cos (x)

y^{^{''}} - 4 y = 8 sin (2 x)

y^{^{''}} + 3 y^{^{'}} - 1 = 0