y^{''}+0.7y+4=cos(3t)

Lösung

y^{^{''}} + 0.7 y + 4 = cos (3 t)

y = c_{1} cos (\frac{7}{10} t) + c_{2} sin (\frac{7}{10} t) - \frac{10}{83} cos (3 t) - \frac{40}{7}

Schritte zur Lösung

y^{''} (t) + 0.7 y + 4 = cos (3 t)

Solve linear ODE:

y = c_{1} cos (\frac{7}{10} t) + c_{2} sin (\frac{7}{10} t) - \frac{10}{83} cos (3 t) - \frac{40}{7}

y = c_{1} cos (\frac{7}{10} t) + c_{2} sin (\frac{7}{10} t) - \frac{10}{83} cos (3 t) - \frac{40}{7}

y^{^{''}} - 4 y^{^{'}} + 3 y = e^{2 t}

1 y^{^{''}} + 5 y^{^{'}} + \frac{1}{\frac{1}{6}} y = 2 e^{2 t}

y^{^{''}} + 2 y^{^{'}} - 2 y = 5 sin (x) - 10 x e^{x}

y^{^{''}} - 8 y^{^{'}} + 17 y = - 102, y (0) = - 3, y^{^{'}} (0) = 8

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3} x ln (x)