y^{''}-8y^'+16y=(12e^{4t})/((t^2+1))

Lösung

y^{^{''}} - 8 y^{^{'}} + 16 y = \frac{12 e ^{4 t}}{( t ^{2} + 1 )}

y = c_{1} e^{4 t} + c_{2} t e^{4 t} - 6 e^{4 t} ln (t^{2} + 1) + 12 e^{4 t} t arctan (t)

Schritte zur Lösung

y^{''} (t) - 8 y^{'} (t) + 16 y = \frac{12 e ^{4 t}}{( t ^{2} + 1 )}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} t e^{4 t} - 6 e^{4 t} ln (t^{2} + 1) + 12 e^{4 t} t arctan (t)

y = c_{1} e^{4 t} + c_{2} t e^{4 t} - 6 e^{4 t} ln (t^{2} + 1) + 12 e^{4 t} t arctan (t)

t an g e n t y = sin (x) cos (x), at x = \frac{3 π}{4}

θ \to \frac{π}{2} lim (3 sin (θ))

\frac{d}{d x} (3 x^{2} - 8)

t an g e n t f (x) = 2 x^{2} - 7 x + 5, at x = 2

\int \frac{1}{x ( 1000 - x )} d x