y^{''}-y^'-6y=12x-e^x,y(0)=1

Lösung

y^{^{''}} - y^{^{'}} - 6 y = 12 x - e^{x}, y (0) = 1

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

Schritte zur Lösung

y^{''} (x) - y^{'} (x) - 6 y = 12 x - e^{x}

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 2 x

\frac{d ^{2} y}{d x ^{2}} + y = sec (x) tan (x)

y^{^{''}} + y + y = \frac{( e ^{t} )}{t}

y^{^{''}} - 4 y^{^{'}} + 3 y = 13 cos (2 x)

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = t e^{3} + 1