3y^{''}-6y^'+6y=exsec(x)

Lösung

3 y^{^{''}} - 6 y^{^{'}} + 6 y = e x sec (x)

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{e sin ( x ) ( - x - 1 ) + 3 e ^{x} cos ( x ) \cdot \int - \frac{e ^{1 - x} x t a n ( x )}{3} d x}{3}

Schritte zur Lösung

3 y^{''} (x) - 6 y^{'} (x) + 6 y = e x sec (x)

Solve linear ODE:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{e sin ( x ) ( - x - 1 ) + 3 e ^{x} cos ( x ) \cdot \int - \frac{e ^{1 - x} x t a n ( x )}{3} d x}{3}

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{e sin ( x ) ( - x - 1 ) + 3 e ^{x} cos ( x ) \cdot \int - \frac{e ^{1 - x} x t a n ( x )}{3} d x}{3}

(D^{2} + 4) y = 5 e^{x} - 4 x^{2}

y^{^{''}} + 2 y = 3 x + 5

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

y^{^{''}} + k y = t^{2} e^{3 t}, y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} + 2 y^{^{'}} + y = t^{2}, y (0) = 1, y^{^{'}} (0) = 1