(2D^2-3D+1)y=csc(2pix)

解

(2 D^{2} - 3 D + 1) y = csc (2 π x)

y = c_{1} e^{x} + c_{2} e^{\frac{x}{2}} + e^{x} \cdot \int \frac{csc ( 2 π x )}{e ^{x}} d x + e^{\frac{x}{2}} \cdot \int - \frac{csc ( 2 π x )}{e ^{\frac{x}{2}}} d x

解答ステップ

(2 D^{2} - 3 D + 1) y = csc (2 π x)

線形 ODE を解く:

y = c_{1} e^{x} + c_{2} e^{\frac{x}{2}} + e^{x} \cdot \int \frac{csc ( 2 π x )}{e ^{x}} d x + e^{\frac{x}{2}} \cdot \int - \frac{csc ( 2 π x )}{e ^{\frac{x}{2}}} d x

y = c_{1} e^{x} + c_{2} e^{\frac{x}{2}} + e^{x} \cdot \int \frac{csc ( 2 π x )}{e ^{x}} d x + e^{\frac{x}{2}} \cdot \int - \frac{csc ( 2 π x )}{e ^{\frac{x}{2}}} d x