(d^2-3d+2)y=5e^3x

Lösung

(d^{2} - 3 d + 2) y = 5 e^{3} x

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{5 e ^{3} x}{2} + \frac{15 e ^{3}}{4}

Schritte zur Lösung

(d^{2} - 3 d + 2) y = 5 e^{3} x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{5 e ^{3} x}{2} + \frac{15 e ^{3}}{4}

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{5 e ^{3} x}{2} + \frac{15 e ^{3}}{4}

(d^{2} - 4 d + 4) y = 8 x^{2} e^{2} x

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

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

(d^{2} + 4 d + 5) y = x^{3}

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