(dy)/(dx)y=6arcsec(x+5)

Lösung

\frac{d y}{d x} y = 6 arcsec (x + 5)

y = 12 (arcsec (x + 5) (x + 5) - ln (x + 5 + x^{2} + 10 x + 24)) + c_{1}, y = - 12 (arcsec (x + 5) (x + 5) - ln (x + 5 + x^{2} + 10 x + 24)) + c_{1}

Schritte zur Lösung

\frac{d y}{d x} y = 6 arcsec (x + 5)

Solve separable ODE:

y = 12 (arcsec (x + 5) (x + 5) - ln (x + 5 + x^{2} + 10 x + 24)) + c_{1}, y = - 12 (arcsec (x + 5) (x + 5) - ln (x + 5 + x^{2} + 10 x + 24)) + c_{1}

y = 12 (arcsec (x + 5) (x + 5) - ln (x + 5 + x^{2} + 10 x + 24)) + c_{1}, y = - 12 (arcsec (x + 5) (x + 5) - ln (x + 5 + x^{2} + 10 x + 24)) + c_{1}

\frac{d y}{d t} = \frac{t + 3 t ^{2}}{y ^{2}}, y (0) = 6

\frac{d y}{d x} = \frac{x ^{2} + 1}{x y}

d y = (y + 1) (1 - x) d x, f (1) = 0

\frac{d S}{d t} = 2 - \frac{S}{10}

x^{\frac{1}{2}} d y - y^{- \frac{3}{2}} d x = 0