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

Lösung

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

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} + c_{4} x - \frac{x ^{4}}{48} - \frac{x ^{2}}{16}

Schritte zur Lösung

y^{(4)} (x) - 4 y^{''} (x) = x^{2}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} + c_{4} x - \frac{x ^{4}}{48} - \frac{x ^{2}}{16}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} + c_{4} x - \frac{x ^{4}}{48} - \frac{x ^{2}}{16}

y^{^{''}} - 4 y^{^{'}} + 8 y = x^{3}

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

2 y^{^{''}} - 7 y^{^{'}} - 4 y = 7 - 2 x

y^{^{''}} + 3 y^{^{'}} = sin (3 x)

y^{^{''}} + 16 y = 5 sin (x)