y^{'''}-19y^'+30y=x^2*e^{2x}

Lösung

y^{^{'''}} - 19 y^{^{'}} + 30 y = x^{2} \cdot e^{2 x}

y = c_{1} e^{2 x} + c_{2} e^{3 x} + c_{3} e^{- 5 x} - \frac{e ^{2 x} x ^{3}}{21} - \frac{6 e ^{2 x} x ^{2}}{49} - \frac{86 e ^{2 x} x}{343}

Schritte zur Lösung

y^{'''} (x) - 19 y^{'} (x) + 30 y = x^{2} \cdot e^{2 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{3 x} + c_{3} e^{- 5 x} - \frac{e ^{2 x} x ^{3}}{21} - \frac{6 e ^{2 x} x ^{2}}{49} - \frac{86 e ^{2 x} x}{343}

y = c_{1} e^{2 x} + c_{2} e^{3 x} + c_{3} e^{- 5 x} - \frac{e ^{2 x} x ^{3}}{21} - \frac{6 e ^{2 x} x ^{2}}{49} - \frac{86 e ^{2 x} x}{343}

y^{^{''}} - 4 y^{^{'}} - 5 y = 125, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = (1 + 2 x) e^{x}

y^{^{''}} - y = \frac{1}{e ^{x} + 1}

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

y^{^{''}} + 2 y^{^{'}} + y = 2 e^{- t}, y (0) = 1, y^{^{'}} (0) = 0