y^{''}-y^'+1/4 y=7+e^{x/2}

Lösung

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 7 + e^{\frac{x}{2}}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 28 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

Schritte zur Lösung

y^{''} (x) - y^{'} (x) + \frac{1}{4} y = 7 + e^{\frac{x}{2}}

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 28 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 28 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

\int t (t^{6} + t - 5) d t

x \to \infty lim (3 e^{- 3 x})

d er i v a t i v e f (x) = (x^{3} - 5 x) (5 x^{2} + 3 x)

\frac{\partial}{\partial x} ([A x^{2} + B y^{3}]^{\frac{1}{4}})

\frac{d}{d x} (\frac{6}{x} - 2)