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

Lösung

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

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{3 x sin ( 2 x )}{20} - \frac{x cos ( 2 x )}{20} - \frac{7}{200} sin (2 x) - \frac{3}{25} cos (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{3 x sin ( 2 x )}{20} - \frac{x cos ( 2 x )}{20} - \frac{7}{200} sin (2 x) - \frac{3}{25} cos (2 x)

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{3 x sin ( 2 x )}{20} - \frac{x cos ( 2 x )}{20} - \frac{7}{200} sin (2 x) - \frac{3}{25} cos (2 x)

y^{^{''}} - y^{^{'}} - 64 y = 54 cos (3 x)

y^{^{'''}} - 5 y^{^{'}} + 6 y^{^{'}} = 9 + 5 sin (x)

(d + 2) (d - 1)^{2} y = e^{- 2} x + 2 sinh (x)

\frac{1}{2} y^{^{''}} + 2 y = 2 tan (2 t) - \frac{1}{2} e^{2 t}

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = 2 e^{- x} + cos (x)