3y^{''}-5y^'-2y=x^3-2x

Lösung

3 y^{^{''}} - 5 y^{^{'}} - 2 y = x^{3} - 2 x

y = c_{1} e^{2 x} + c_{2} e^{- \frac{x}{3}} - \frac{x ^{3}}{2} + \frac{15 x ^{2}}{4} - \frac{89 x}{4} + \frac{535}{8}

Schritte zur Lösung

3 y^{''} (x) - 5 y^{'} (x) - 2 y = x^{3} - 2 x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- \frac{x}{3}} - \frac{x ^{3}}{2} + \frac{15 x ^{2}}{4} - \frac{89 x}{4} + \frac{535}{8}

y = c_{1} e^{2 x} + c_{2} e^{- \frac{x}{3}} - \frac{x ^{3}}{2} + \frac{15 x ^{2}}{4} - \frac{89 x}{4} + \frac{535}{8}

x \to - 2 lim (x^{3} - 2 x^{2} + 1)

\frac{d}{d x} (arctan (x - 5))

d er i v a t i v e \frac{2 x - 1}{2 x + 3}

\int \frac{x ^{4} + 1}{x ^{3} - x ^{2}} d x

\int_{7}^{9} \frac{y}{y ^{2} - 3 y - 4} d y