(d^2-8d+9)y=8sin^5(x)

Lösung

(d^{2} - 8 d + 9) y = 8 sin^{5} (x)

y = c_{1} e^{(4 + 7) x} + c_{2} e^{(4 - 7) x} + e^{4 x + 7 x} \cdot \int \frac{4 7 e ^{- 4 x - 7 x} sin ^{5} ( x )}{7} d x + e^{4 x - 7 x} \cdot \int - \frac{4 7 e ^{- 4 x + 7 x} sin ^{5} ( x )}{7} d x

Schritte zur Lösung

(d^{2} - 8 d + 9) y = 8 sin^{5} (x)

Solve linear ODE:

y = c_{1} e^{(4 + 7) x} + c_{2} e^{(4 - 7) x} + e^{4 x + 7 x} \cdot \int \frac{4 7 e ^{- 4 x - 7 x} sin ^{5} ( x )}{7} d x + e^{4 x - 7 x} \cdot \int - \frac{4 7 e ^{- 4 x + 7 x} sin ^{5} ( x )}{7} d x

y = c_{1} e^{(4 + 7) x} + c_{2} e^{(4 - 7) x} + e^{4 x + 7 x} \cdot \int \frac{4 7 e ^{- 4 x - 7 x} sin ^{5} ( x )}{7} d x + e^{4 x - 7 x} \cdot \int - \frac{4 7 e ^{- 4 x + 7 x} sin ^{5} ( x )}{7} d x

(d^{2} + 5 d + 6) \cdot y = x^{2}

(d^{3} + 8) y = x^{4} + 2 x + 1

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

(d^{2} - 1) y = x^{2} cos (x)

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 cosh (x)