y^{''}-5y^'=(8t-7)sin(2t)

Lösung

y^{^{''}} - 5 y^{^{'}} = (8 t - 7) sin (2 t)

y = c_{1} e^{5 t} + c_{2} + \frac{20 t cos ( 2 t )}{29} - \frac{8 t sin ( 2 t )}{29} - \frac{167}{841} sin (2 t) - \frac{1079}{1682} cos (2 t)

Schritte zur Lösung

y^{''} (t) - 5 y^{'} (t) = (8 t - 7) sin (2 t)

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} + \frac{20 t cos ( 2 t )}{29} - \frac{8 t sin ( 2 t )}{29} - \frac{167}{841} sin (2 t) - \frac{1079}{1682} cos (2 t)

y = c_{1} e^{5 t} + c_{2} + \frac{20 t cos ( 2 t )}{29} - \frac{8 t sin ( 2 t )}{29} - \frac{167}{841} sin (2 t) - \frac{1079}{1682} cos (2 t)

x \to 7 lim (x (x - 2))

\frac{d}{d x} (cos (5 x^{2} + 7 x - 1))

d er i v a t i v e 2 x \cdot cos (x^{2})

\int \frac{1}{1 0 ^{x}} d x

\int \frac{x ^{4}}{3355} d x