y^{''''}+y^{''}=7x-3cos(x)

Lösung

y^{^{''''}} + y^{^{''}} = 7 x - 3 cos (x)

y = c_{1} + c_{2} x + c_{3} cos (x) + c_{4} sin (x) + \frac{7 x ^{3}}{6} + \frac{3 x sin ( x )}{2}

Schritte zur Lösung

y^{(4)} (x) + y^{''} (x) = 7 x - 3 cos (x)

Solve linear ODE:

y = c_{1} + c_{2} x + c_{3} cos (x) + c_{4} sin (x) + \frac{7 x ^{3}}{6} + \frac{3 x sin ( x )}{2}

y = c_{1} + c_{2} x + c_{3} cos (x) + c_{4} sin (x) + \frac{7 x ^{3}}{6} + \frac{3 x sin ( x )}{2}

2 y^{^{'''}} + 3 y^{^{''}} - 3 y^{^{'}} - 2 y = e^{- t}

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{16 e ^{- 3 x}}{x ^{2} + 1}

y^{^{''}} - 2 y^{^{'}} = 30 e^{- 3 t}

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

y^{^{''}} + 4 y^{^{'}} + 3 y = 6 + e^{2 t}