y^{'''}+3y^{''}-4y^'-12y=4cos(x)

Lösung

y^{^{'''}} + 3 y^{^{''}} - 4 y^{^{'}} - 12 y = 4 cos (x)

y = c_{1} e^{- 3 x} + c_{2} e^{- 2 x} + c_{3} e^{2 x} - \frac{2}{25} sin (x) - \frac{6}{25} cos (x)

Schritte zur Lösung

y^{'''} (x) + 3 y^{''} (x) - 4 y^{'} (x) - 12 y = 4 cos (x)

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} e^{- 2 x} + c_{3} e^{2 x} - \frac{2}{25} sin (x) - \frac{6}{25} cos (x)

y = c_{1} e^{- 3 x} + c_{2} e^{- 2 x} + c_{3} e^{2 x} - \frac{2}{25} sin (x) - \frac{6}{25} cos (x)

y^{^{'''}} - a y^{^{'}} = 1 + cosh (a x)

y^{^{''}} + 5 y^{^{'}} + 8 y = 24 + 23 x + 12 x^{2}

4 y^{^{''}} - y = 1, y^{^{'}} (0) = \frac{1}{2}

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

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 x} ln (x^{2} + 1)