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

Lösung

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

y = c_{1} e^{3 t} + c_{2} + \frac{t cos ( 3 t )}{6} - \frac{t sin ( 3 t )}{6} + \frac{7}{18} cos (3 t) - \frac{5}{9} sin (3 t)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} + \frac{t cos ( 3 t )}{6} - \frac{t sin ( 3 t )}{6} + \frac{7}{18} cos (3 t) - \frac{5}{9} sin (3 t)

y = c_{1} e^{3 t} + c_{2} + \frac{t cos ( 3 t )}{6} - \frac{t sin ( 3 t )}{6} + \frac{7}{18} cos (3 t) - \frac{5}{9} sin (3 t)

d er i v a t i v e \frac{f ( x ) g ( x )}{x}

y \frac{d y}{d x} + 3 y = x^{2} y

d er i v a t i v e x^{7 x}

\int cos (x) (1 + 5 sin^{2} (x)) d x

n = 0 \sum \infty \frac{1}{n ^{2} + n + 1}