y^{'''}-3y^{''}=e^{2x}

Lösung

y^{^{'''}} - 3 y^{^{''}} = e^{2 x}

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + y = e^{x} + x^{3}, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} - 4 y = x^{- 1} e^{2 x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} 4 + 8 y = 8 x^{2} + 8 x + 1

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 y = x^{2} + x + 1

y^{^{'''}} + y = 2 x^{2} + 9