y^{''}+9y=e^t

Lösung

y^{^{''}} + 9 y = e^{t}

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{10} e^{t}

Schritte zur Lösung

y^{''} (t) + 9 y = e^{t}

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{10} e^{t}

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{10} e^{t}

y^{^{''}} + y^{^{'}} - 6 y = x

y^{^{''}} - 7 y^{^{'}} + a = 0, y (0) = 1, y^{^{'}} (0) = 10

y^{^{''}} + 4 y = - 6, y (\frac{π}{8}) = - \frac{1}{2}, y^{^{'}} (\frac{π}{8}) = 2

y^{^{''}} - 4 y^{^{'}} + 8 y = 8 x^{2} - 2

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