y^{''}-4y^'+3y=xcos(x)

Lösung

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

y = c_{1} e^{3 x} + c_{2} e^{x} - \frac{x sin ( x )}{5} + \frac{x cos ( x )}{10} - \frac{11}{50} sin (x) - \frac{1}{25} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{x} - \frac{x sin ( x )}{5} + \frac{x cos ( x )}{10} - \frac{11}{50} sin (x) - \frac{1}{25} cos (x)

y = c_{1} e^{3 x} + c_{2} e^{x} - \frac{x sin ( x )}{5} + \frac{x cos ( x )}{10} - \frac{11}{50} sin (x) - \frac{1}{25} cos (x)

y^{^{''}} + y = \frac{cos ( x ) + 1}{sin ( x )}

y^{^{''}} + y^{^{'}} = 1, y^{1} (0) = 1

y^{^{''}} + 2 y^{^{'}} - 3 y = sin (t)

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

y^{^{''}} + y^{^{'}} - 2 y = 8 sin (2 x)