y^{''}-y^'+y=2sin(3x)

Lösung

y^{^{''}} - y^{^{'}} + y = 2 sin (3 x)

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) - \frac{16}{73} sin (3 x) + \frac{6}{73} cos (3 x)

Schritte zur Lösung

y^{''} (x) - y^{'} (x) + y = 2 sin (3 x)

Solve linear ODE:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) - \frac{16}{73} sin (3 x) + \frac{6}{73} cos (3 x)

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) - \frac{16}{73} sin (3 x) + \frac{6}{73} cos (3 x)

d er i v a t i v e \frac{- x sin ( x ) - cos ( x )}{6 x ^{2}}

\frac{d y}{d x} = x e^{x}

t an g e n t f (x) = - 3 x^{2} - 4 x - 2, at x = 2

\int x x + 1 d x

\int_{0}^{1} 4 cos (\frac{π t}{2}) d t