y^{''}-2y^'=8sin(2x)+2xe^{2x}

Lösung

y^{^{''}} - 2 y^{^{'}} = 8 sin (2 x) + 2 x e^{2 x}

y = c_{1} e^{2 x} + c_{2} - cos (2 x) - sin (2 x) + \frac{1}{2} e^{2 x} x^{2} - 4 sin^{2} (x) - \frac{1}{2} e^{2 x} x + \frac{1}{4} e^{2 x}

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) = 8 sin (2 x) + 2 x e^{2 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} - cos (2 x) - sin (2 x) + \frac{1}{2} e^{2 x} x^{2} - 4 sin^{2} (x) - \frac{1}{2} e^{2 x} x + \frac{1}{4} e^{2 x}

y = c_{1} e^{2 x} + c_{2} - cos (2 x) - sin (2 x) + \frac{1}{2} e^{2 x} x^{2} - 4 sin^{2} (x) - \frac{1}{2} e^{2 x} x + \frac{1}{4} e^{2 x}

\frac{d}{d x} (\frac{9}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}})

\frac{\partial}{\partial x} (e^{x y} + \frac{1}{x + y})

t an g e n t 4 x^{2} + 2 x - 1

f (x) = (5 x^{6} + 4 x^{3})^{4}

\frac{\partial}{\partial x} (ln (8 x + 7 y))