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

Lösung

y^{^{'''}} - 19 y^{^{'}} + 30 y = x^{2} 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} 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^{^{''}} - y^{^{'}} + 144 y = 12 sin (12 t)

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

y^{^{''}} - 4 y = 1

y^{^{''}} - 4 y = 5

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = x^{2} + 1