(d^2x)/(dt^2)+(dx)/(dt)+x=0.5sin(2t)

Lösung

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} + x = 0.5 sin (2 t)

x = e^{- \frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) - 0.11538 \dots sin (2 t) - \frac{1}{13} cos (2 t)

Schritte zur Lösung

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} + x = 0.5 sin (2 t)

Solve linear ODE:

x = e^{- \frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) - 0.11538 \dots sin (2 t) - \frac{1}{13} cos (2 t)

x = e^{- \frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) - 0.11538 \dots sin (2 t) - \frac{1}{13} cos (2 t)

\int \frac{1}{x ^{2} - 25} d x

\int (\frac{3}{x ^{2}}) d x

\int \frac{2}{3} x^{2} ln (x) d x

x \to 1 lim (\frac{( x ^{2} - 5 )}{x})

x \to 5 lim (8 x + 5)