y^{''}-8y^'+16y=8x+7

Lösung

y^{^{''}} - 8 y^{^{'}} + 16 y = 8 x + 7

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{x}{2} + \frac{11}{16}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 16 y = 8 x + 7

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{x}{2} + \frac{11}{16}

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{x}{2} + \frac{11}{16}

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

y^{^{''}} - 16 y = (x + 1) e^{x}

y^{^{''}} + 9 y = 13 e^{2 x} + 10 sin (2 x)

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

y^{^{''}} + 4 y^{^{'}} + 3 y = 1