(d^2y)/(dx^2)-6y=e^{3x}(x^2+2)

Lösung

\frac{d ^{2} y}{d x ^{2}} - 6 y = e^{3 x} (x^{2} + 2)

y = c_{1} e^{6 x} + c_{2} e^{- 6 x} + \frac{e ^{3 x} x ^{2}}{3} - \frac{4 e ^{3 x} x}{3} + \frac{28}{9} e^{3 x}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 6 y = e^{3 x} (x^{2} + 2)

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- 6 x} + \frac{e ^{3 x} x ^{2}}{3} - \frac{4 e ^{3 x} x}{3} + \frac{28}{9} e^{3 x}

y = c_{1} e^{6 x} + c_{2} e^{- 6 x} + \frac{e ^{3 x} x ^{2}}{3} - \frac{4 e ^{3 x} x}{3} + \frac{28}{9} e^{3 x}

2 y^{^{''}} + y^{^{'}} + 2 y = 1, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + y = (sec (x))^{2}

2 q^{^{''}} + 10 q^{^{'}} + 12 q = e^{- 3 t}

\frac{d ^{2} y}{d x ^{2}} + 12 \frac{d y}{d x} + 32 y = 160

y^{^{''}} - 4 y^{^{'}} = 16 t + 36, y (- 2) = 2, y^{^{'}} (- 2) = - 1