y^{''}+4y^'=(4t-4)sin(3t)

Lösung

y^{^{''}} + 4 y^{^{'}} = (4 t - 4) sin (3 t)

y = c_{1} + c_{2} e^{- 4 t} - \frac{4 t sin ( 3 t )}{25} - \frac{16 t cos ( 3 t )}{75} + \frac{1588}{5625} sin (3 t) + \frac{328}{1875} cos (3 t)

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) = (4 t - 4) sin (3 t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 4 t} - \frac{4 t sin ( 3 t )}{25} - \frac{16 t cos ( 3 t )}{75} + \frac{1588}{5625} sin (3 t) + \frac{328}{1875} cos (3 t)

y = c_{1} + c_{2} e^{- 4 t} - \frac{4 t sin ( 3 t )}{25} - \frac{16 t cos ( 3 t )}{75} + \frac{1588}{5625} sin (3 t) + \frac{328}{1875} cos (3 t)

n = 0 \sum \infty 0. 8^{n}

d er i v a t i v e e^{x} (x + x x)

\frac{d}{d x} (ln (\frac{5 x ^{2} + x + 6}{x ^{3}}))

\int_{0}^{1} 12 e^{3 x} d x

in v erse l a pl a ce \frac{s}{s ^{2} + 2 \cdot 3 \cdot π \cdot s + π ^{2}}