y^{''}-6y^'+25y=-45cos(2t)+30sin(2t)

Lösung

y^{^{''}} - 6 y^{^{'}} + 25 y = - 45 cos (2 t) + 30 sin (2 t)

y = e^{3 t} (c_{1} cos (4 t) + c_{2} sin (4 t)) + 2 sin (2 t) - cos (2 t)

Schritte zur Lösung

y^{''} (t) - 6 y^{'} (t) + 25 y = - 45 cos (2 t) + 30 sin (2 t)

Solve linear ODE:

y = e^{3 t} (c_{1} cos (4 t) + c_{2} sin (4 t)) + 2 sin (2 t) - cos (2 t)

y = e^{3 t} (c_{1} cos (4 t) + c_{2} sin (4 t)) + 2 sin (2 t) - cos (2 t)

\frac{d}{d x} (ln (coth (x)))

\int \frac{cos ( 5 x )}{e ^{s i n (5 x)}} d x

\frac{d y}{d x} = 9 x + y

x \to 0 lim ((x - 1)^{2})

\int_{0}^{\infty} x^{2} e^{- x} d x