(d^3+8)y=x^4+2x+1

Lösung

(d^{3} + 8) y = x^{4} + 2 x + 1

y = c_{1} e^{- 2 x} + e^{x} (c_{2} cos (3 x) + c_{3} sin (3 x)) + \frac{x ^{4}}{8} - \frac{x}{8} + \frac{1}{8}

Schritte zur Lösung

(d^{3} + 8) y = x^{4} + 2 x + 1

Solve linear ODE:

y = c_{1} e^{- 2 x} + e^{x} (c_{2} cos (3 x) + c_{3} sin (3 x)) + \frac{x ^{4}}{8} - \frac{x}{8} + \frac{1}{8}

y = c_{1} e^{- 2 x} + e^{x} (c_{2} cos (3 x) + c_{3} sin (3 x)) + \frac{x ^{4}}{8} - \frac{x}{8} + \frac{1}{8}

d \cdot e (d^{2} - 4) y = (e^{2})^{x}

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

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 cosh (x)

(d^{3} - 6 d^{2} + 11 d - 6) y = e - 2 x + e - 3 x

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