4y^{''}+5y^'+2y=-2x^2+x

Lösung

4 y^{^{''}} + 5 y^{^{'}} + 2 y = - 2 x^{2} + x

y = e^{- \frac{5 x}{8}} (c_{1} cos (\frac{7 x}{8}) + c_{2} sin (\frac{7 x}{8})) - x^{2} + \frac{11 x}{2} - \frac{39}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- \frac{5 x}{8}} (c_{1} cos (\frac{7 x}{8}) + c_{2} sin (\frac{7 x}{8})) - x^{2} + \frac{11 x}{2} - \frac{39}{4}

y = e^{- \frac{5 x}{8}} (c_{1} cos (\frac{7 x}{8}) + c_{2} sin (\frac{7 x}{8})) - x^{2} + \frac{11 x}{2} - \frac{39}{4}

y^{^{''}} - y^{^{'}} + y = 2 cos (2 x) - 3 sin (2 x)

y^{^{'''}} + 4 y^{^{''}} - 9 y^{^{'}} - 36 = x^{2} - 4

y^{^{''}} + y = \frac{1}{( cos ( x ) )}

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

y^{^{''}} + 8 y^{^{'}} + 16 y = x