(d^2y)/(dx^2)-2(dy)/(dx)+y=x^2e^x

Lösung

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

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{x} x ^{4}}{12}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{x} x ^{4}}{12}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{x} x ^{4}}{12}

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} - 3 y = e^{t}

y^{^{''}} + 8 y^{^{'}} + 17 y = 6 e^{- 40} cos (t)

y^{^{''}} + \frac{3}{2} y^{^{'}} = x + e^{2 x}

\frac{d ^{4} y}{d x ^{4}} + 6 \frac{d y}{d x} = - 5 x^{2}

y^{^{''}} + y^{^{'}} - 8 y = 9 e^{3 t}