(d^2y)/(dx^2)+y=xcos(2x)

Lösung

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

y = c_{1} cos (x) + c_{2} sin (x) - \frac{x cos ( 2 x )}{3} + \frac{4}{9} sin (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - \frac{x cos ( 2 x )}{3} + \frac{4}{9} sin (2 x)

y = c_{1} cos (x) + c_{2} sin (x) - \frac{x cos ( 2 x )}{3} + \frac{4}{9} sin (2 x)

y^{^{''}} + 2 y^{^{'}} = x^{2} + 3 x^{2} e^{- 2 x} + e^{2 x} + 1

y^{^{''}} - 8 y^{^{'}} + 12 y = e^{2 x} (x^{2} - 1)

y^{^{''}} + y^{^{'}} - 12 y = 2 t e - 4 t, y (0) = - 5, y^{^{'}} (0) = - 4

y^{^{''}} + 25 y = 5 tan^{2} (5 x) cos (5 x)

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