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

Lösung

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

Schritte zur Lösung

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

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

(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}