(d^2y)/(dx^2)-y=xe^{2x}

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

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

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 x

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{2 x} + 1

y^{^{''}} - y^{^{'}} - 2 y = 5 e^{4 x} + 6 x

y^{^{''}} + 4 y - 5 = 0