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

Lösung

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

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{1}{10} e^{x} cos (2 x) - \frac{1}{5} e^{x} sin (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{1}{10} e^{x} cos (2 x) - \frac{1}{5} e^{x} sin (2 x)

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{1}{10} e^{x} cos (2 x) - \frac{1}{5} e^{x} sin (2 x)

\frac{\partial}{\partial x} (arctan (2 x y))

\int \frac{( e ^{x} - e ^{- x} )}{e ^{2 x}} d x

\frac{\partial}{\partial s} (s cos (t))

\frac{d}{d x} (x^{2} - 4 - 2 arcsec (\frac{x}{2}))

x \to \infty lim (e^{5 x l n (1 + \frac{1}{x})})