(d^2-3d+4)y=sin(x)+e^x

Lösung

(d^{2} - 3 d + 4) y = sin (x) + e^{x}

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

Schritte zur Lösung

(d^{2} - 3 d + 4) y = sin (x) + e^{x}

Solve linear ODE:

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

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

(d^{2} - 2 d + 5) \cdot y = e^{2} x sin (x)

y^{^{''}} + 8 y^{^{'}} + 16 y = x^{2}

(d^{3} - 3 d + 2) \cdot y = x

y^{^{'''}} - 4 y^{^{''}} = 2 x + 3

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