y^{''}+5y=e^{2x}-x-x^2+x^3

Lösung

y^{^{''}} + 5 y = e^{2 x} - x - x^{2} + x^{3}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{1}{9} e^{2 x} + \frac{x ^{3} - x ^{2}}{5} + \frac{- 11 x + 2}{25}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{1}{9} e^{2 x} + \frac{x ^{3} - x ^{2}}{5} + \frac{- 11 x + 2}{25}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{1}{9} e^{2 x} + \frac{x ^{3} - x ^{2}}{5} + \frac{- 11 x + 2}{25}

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 6 e^{x}

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

y^{^{''}} + y = \frac{sin ( x )}{( cos ( x ) ) ^{2}}

y^{^{''}} + 9 y = 2 sin (x)

y^{^{''}} + 14 y^{^{'}} + 49 y = e^{- 7 t} ln (t)