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

Lösung

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

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{7 x}{4}) + c_{2} sin (\frac{7 x}{4})) + \frac{1}{2} sin (x) - \frac{1}{2} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{7 x}{4}) + c_{2} sin (\frac{7 x}{4})) + \frac{1}{2} sin (x) - \frac{1}{2} cos (x)

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{7 x}{4}) + c_{2} sin (\frac{7 x}{4})) + \frac{1}{2} sin (x) - \frac{1}{2} cos (x)

(d - 2)^{2} y = 3 e^{2} x + 5 e

y^{^{'''}} - 3 y^{^{'}} + 2 y = 9 e^{x}

y^{^{''}} - 6 y^{^{'}} + 5 y = 3^{x}

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

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