y^{''}-xe^{-x}=2y^'

Lösung

y^{^{''}} - x e^{- x} = 2 y^{^{'}}

y = c_{1} e^{2 x} + c_{2} + \frac{e ^{- x} x}{3} + \frac{4}{9} e^{- x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} + \frac{e ^{- x} x}{3} + \frac{4}{9} e^{- x}

y = c_{1} e^{2 x} + c_{2} + \frac{e ^{- x} x}{3} + \frac{4}{9} e^{- x}

y^{^{''}} + 4 y = 3, 2 sin (4 t) y (0) = 1

x^{^{''}} + 4 x = - t^{2}

y^{^{''}} + y = 5 sec^{3} (x)

4 y^{^{''}} - 16 y = 4 x

x^{^{''}} + 2 x = 2 t + 26