y^{''}-3y^'+2y=ex

Lösung

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

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{e x}{2} + \frac{3 e}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{e x}{2} + \frac{3 e}{4}

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{e x}{2} + \frac{3 e}{4}

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

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

y^{^{''}} - 4 y^{^{'}} = 4 x

y^{^{''}} - 5 y^{^{'}} + 7 y = x e^{x}

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