(d^2+d+1)y=x^3

Lösung

(d^{2} + d + 1) y = x^{3}

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

Schritte zur Lösung

(d^{2} + d + 1) y = x^{3}

Solve linear ODE:

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

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

(d^{2} - 3 d + 2) y = 3 sin^{2} (x)

(d^{2} + 3 d + 2) y = 4 cos^{2} (x)

y^{^{''}} + 3 y^{^{'}} = - 48 x^{2} e^{3} x

(d^{3} - d^{2} - d + 1) y = 1 + x^{2}

(d^{3} + 4 d) y = 4 cot (2 x)