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

Lösung

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

y = c_{1} e^{3 x} + c_{2} - \frac{3}{10} e^{x} sin (2 x) + \frac{1}{10} e^{x} cos (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} - \frac{3}{10} e^{x} sin (2 x) + \frac{1}{10} e^{x} cos (2 x)

y = c_{1} e^{3 x} + c_{2} - \frac{3}{10} e^{x} sin (2 x) + \frac{1}{10} e^{x} cos (2 x)

d er i v a t i v e f (x) = \frac{x - 7}{9 x ^{2} e ^{x}}

\frac{\partial}{\partial x} ((e^{x} - 3) sin (y))

d er i v a t i v e \frac{3}{x ^{2}} - 8 4 x

\frac{d}{d x} ((3 x + 2) (4 x - 3))

\frac{d}{d x} ((x^{3} - 4 x) \cdot e^{3 x})