y^{''}-y^'+1/4 y=3+e^{x/2}

Lösung

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 3 + e^{\frac{x}{2}}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 12 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

Schritte zur Lösung

y^{''} (x) - y^{'} (x) + \frac{1}{4} y = 3 + e^{\frac{x}{2}}

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 12 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 12 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

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

\int 2 e^{2 x} sec^{3} (e^{2 x}) d x

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

\int_{0}^{1} 1 + 36 x d x

\int cos^{3} (2 θ) sin (2 θ) d θ