(d^2+d-6)y=e^2x*sin^3(x)

Lösung

(d^{2} + d - 6) y = e^{2} x \cdot sin^{3} (x)

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + e^{2 x} \cdot \int \frac{e ^{- 2 x + 2} x sin ^{3} ( x )}{5} d x + e^{- 3 x} \cdot \int - \frac{e ^{3 x + 2} x sin ^{3} ( x )}{5} d x

Schritte zur Lösung

(d^{2} + d - 6) y = e^{2} x sin^{3} (x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + e^{2 x} \cdot \int \frac{e ^{- 2 x + 2} x sin ^{3} ( x )}{5} d x + e^{- 3 x} \cdot \int - \frac{e ^{3 x + 2} x sin ^{3} ( x )}{5} d x

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + e^{2 x} \cdot \int \frac{e ^{- 2 x + 2} x sin ^{3} ( x )}{5} d x + e^{- 3 x} \cdot \int - \frac{e ^{3 x + 2} x sin ^{3} ( x )}{5} d x

y^{^{''}} + y^{^{'}} - 6 y = 6 x^{2} - 2 x - 2

(d^{2} - 4 d + 4) \cdot y = x^{3}

(d^{3} - 25 d) y = sin^{2} (x) cos^{2} (x)

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

y^{^{''}} + y^{^{'}} - 2 y = 14 + 2 x - 2 x^{2}