(d^2y)/(dx^2)-6(dy)/(dx)=12x

Lösung

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} = 12 x

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

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} = 12 x

Solve linear ODE:

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

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

y^{^{''}} + 3 y^{^{'}} = 3 x

y^{^{''}} - y^{^{'}} - 2 y = - 4 x^{2} - 6 x + 1

y^{^{''}} - 4 y^{^{'}} + 5 y = 10 x - 3

y^{^{''}} - 6 y^{^{'}} + 8 y = x e^{x}

- y^{^{''}} - 4 y = t^{2}