y^{''}-4y^'+7y=xe^x

Lösung

y^{^{''}} - 4 y^{^{'}} + 7 y = x e^{x}

y = e^{2 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{e ^{x} x}{4} + \frac{1}{8} e^{x}

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 7 y = x e^{x}

Solve linear ODE:

y = e^{2 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{e ^{x} x}{4} + \frac{1}{8} e^{x}

y = e^{2 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{e ^{x} x}{4} + \frac{1}{8} e^{x}

d er i v a t i v e f (x) = \frac{1}{x ^{31}}

\frac{d}{d x} (ln (3^{x^{2}}))

x \to 4 lim (3 x^{3} - 2 x^{2} + x - 7)

d er i v a t i v e \frac{( 3 x ^{2} )}{4} + \frac{x}{3}

\int \frac{3 - 18 x}{25 - 9 x ^{2}} d x