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

Lösung

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

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{3 x sin ( x )}{10} + \frac{x cos ( x )}{10} - \frac{17}{50} sin (x) - \frac{3}{25} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{3 x sin ( x )}{10} + \frac{x cos ( x )}{10} - \frac{17}{50} sin (x) - \frac{3}{25} cos (x)

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{3 x sin ( x )}{10} + \frac{x cos ( x )}{10} - \frac{17}{50} sin (x) - \frac{3}{25} cos (x)

y^{^{''}} + y = sec (x) csc (x)

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

y^{^{''}} + y^{^{'}} - 2 y + 1 = 0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 = 3 cos (x)

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