x^{''}+x=tsin(2t)

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

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

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

y^{^{''}} - 6 y^{^{'}} + 5 y = t e^{2 t}

y^{^{''}} + 4 y = 6 sin (x)

y^{^{'''}} - 5 y^{^{''}} + 3 y^{^{'}} + 9 = 0