4(d^2y)/(dx^2)-y=x*e^{x/2}

Lösung

4 \frac{d ^{2} y}{d x ^{2}} - y = x \cdot e^{\frac{x}{2}}

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

Schritte zur Lösung

4 \frac{d ^{2} y}{d x ^{2}} - y = x \cdot e^{\frac{x}{2}}

Solve linear ODE:

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

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

y^{^{''}} + 9 y = 18 t

y^{^{''}} + 4 y = cos (2 t) + sin (t)

4 y^{^{''}} + 4 y^{^{'}} + y = 3 x e^{x}

y^{^{''}} - 6 y + 9 = e^{3 x}

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = 4 cos (x)