(d^2y)/(dx^2)-5(dy)/(dx)+6y=x^2+x

Lösung

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

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{4 x}{9} + \frac{17}{54}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{4 x}{9} + \frac{17}{54}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{4 x}{9} + \frac{17}{54}

y^{^{''}} - 4 y^{^{'}} - 12 y = - 20 t + 24 t^{2}

(D^{2} - 1) y = x

y^{^{''}} + 5 y^{^{'}} + 2 y = 9 t + 7

y^{^{''}} + 4 y^{^{'}} = 2

(D^{2} + 5 D + 6) y = e^{2 x}