y^{''}+2y^'=(8t-7)sin(3t)

Lösung

y^{^{''}} + 2 y^{^{'}} = (8 t - 7) sin (3 t)

y = c_{1} + c_{2} e^{- 2 t} - \frac{8 t sin ( 3 t )}{13} - \frac{16 t cos ( 3 t )}{39} + \frac{1315}{1521} sin (3 t) + \frac{38}{507} cos (3 t)

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) = (8 t - 7) sin (3 t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 t} - \frac{8 t sin ( 3 t )}{13} - \frac{16 t cos ( 3 t )}{39} + \frac{1315}{1521} sin (3 t) + \frac{38}{507} cos (3 t)

y = c_{1} + c_{2} e^{- 2 t} - \frac{8 t sin ( 3 t )}{13} - \frac{16 t cos ( 3 t )}{39} + \frac{1315}{1521} sin (3 t) + \frac{38}{507} cos (3 t)

\int e^{2 t} d t

\frac{\partial}{\partial y} (x^{3} cos (y))

x \to 0 lim (5 x^{2})

y \frac{d y}{d x} = x

s l o p e (3, 6), (5, 8)