x^{''}-3x^'=8sin(t)

Lösung

x^{^{''}} - 3 x^{^{'}} = 8 sin (t)

x = c_{1} e^{3 t} + c_{2} - \frac{4}{5} sin (t) + \frac{12}{5} cos (t)

Schritte zur Lösung

x^{''} (t) - 3 x^{'} (t) = 8 sin (t)

Solve linear ODE:

x = c_{1} e^{3 t} + c_{2} - \frac{4}{5} sin (t) + \frac{12}{5} cos (t)

x = c_{1} e^{3 t} + c_{2} - \frac{4}{5} sin (t) + \frac{12}{5} cos (t)

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

y^{^{''}} - y^{^{'}} - 20 y = - 56 t + 40 t^{2}

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

y^{^{''}} + y^{^{'}} + y = e^{x}

y^{^{''}} + y^{^{'}} = e^{t}