(d^2-4)y=xsinh(x)

Lösung

(d^{2} - 4) \cdot y = x \cdot sinh (x)

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + e^{2 x} \cdot \int \frac{e ^{- 2 x} x sinh ( x )}{4} d x + e^{- 2 x} \cdot \int - \frac{e ^{2 x} x sinh ( x )}{4} d x

Schritte zur Lösung

(d^{2} - 4) y = x sinh (x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + e^{2 x} \cdot \int \frac{e ^{- 2 x} x sinh ( x )}{4} d x + e^{- 2 x} \cdot \int - \frac{e ^{2 x} x sinh ( x )}{4} d x

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + e^{2 x} \cdot \int \frac{e ^{- 2 x} x sinh ( x )}{4} d x + e^{- 2 x} \cdot \int - \frac{e ^{2 x} x sinh ( x )}{4} d x

(d^{2} - 2 d + 3) \cdot y = cos (x) + x^{2}

(d^{3} + 3 d^{2} + 2 d) y = x

(d^{2} + 9) y = cos^{2} (x)

(d^{4} - 1) \cdot y = sin (x)

(d^{3} - d^{2} + d - 1) y = 4 sin (x)