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

Lösung

(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

Schritte zur Lösung

(2 D^{2} - 3 D + 1) y = csc (2 π x)

Solve linear ODE:

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

y^{^{''}} - 7 y^{^{'}} = x^{2}

x^{^{''}} + 3 x^{^{'}} + 2 x = 3 cos (2 t)

2 x^{^{''}} + 5 x^{^{'}} + 4 x = 10 r (t)

x^{^{''}} + 6 x^{^{'}} - 4 x = 8 e^{t}

y^{^{''}} + 9 y = 2 cos (3 x) - 3 sin (3 x)