y^{''}-6y^'-2y+1=cos(2x)

Lösung

y^{^{''}} - 6 y^{^{'}} - 2 y + 1 = cos (2 x)

y = c_{1} e^{(3 + 11) x} + c_{2} e^{(3 - 11) x} - \frac{1}{15} sin (2 x) - \frac{1}{30} cos (2 x) + \frac{1}{2}

Schritte zur Lösung

y^{''} (x) - 6 y^{'} (x) - 2 y + 1 = cos (2 x)

Solve linear ODE:

y = c_{1} e^{(3 + 11) x} + c_{2} e^{(3 - 11) x} - \frac{1}{15} sin (2 x) - \frac{1}{30} cos (2 x) + \frac{1}{2}

y = c_{1} e^{(3 + 11) x} + c_{2} e^{(3 - 11) x} - \frac{1}{15} sin (2 x) - \frac{1}{30} cos (2 x) + \frac{1}{2}

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

\int (x - 1)^{4} d x

\int 2 x + 7 d x

t an g e n t x + 1

y^{^{''}} - a y^{^{'}} - b y = 0