y^{''}+y^'=6x+e^x

Lösung

y^{^{''}} + y^{^{'}} = 6 x + e^{x}

y = c_{1} + c_{2} e^{- x} + 3 x^{2} - 6 x + \frac{1}{2} e^{x}

Schritte zur Lösung

y^{''} (x) + y^{'} (x) = 6 x + e^{x}

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + 3 x^{2} - 6 x + \frac{1}{2} e^{x}

y = c_{1} + c_{2} e^{- x} + 3 x^{2} - 6 x + \frac{1}{2} e^{x}

y^{^{''''}} - y = 13 t + cos (t)

y^{^{''}} + 4 y = 2 e^{3 x}

y^{^{''}} + 25 y = 3 csc^{2} (5 t)

\frac{d ^{2} y}{d x ^{2}} - y = x

y^{^{''}} - 3 y^{^{'}} + 2 y = 12