(dy)/(dx)y=ln(ln(2x))

解答

\frac{d y}{d x} y = ln (ln (2 x))

y = 2 x ln (ln (2 x)) - Ei (ln (2 x)) + c_{1}, y = - 2 x ln (ln (2 x)) - Ei (ln (2 x)) + c_{1}

求解步骤

\frac{d y}{d x} y = ln (ln (2 x))

求解可分离方程:

y = 2 x ln (ln (2 x)) - Ei (ln (2 x)) + c_{1}, y = - 2 x ln (ln (2 x)) - Ei (ln (2 x)) + c_{1}

y = 2 x ln (ln (2 x)) - Ei (ln (2 x)) + c_{1}, y = - 2 x ln (ln (2 x)) - Ei (ln (2 x)) + c_{1}

9 y \frac{d y}{d x} = 2 x^{2}

x y^{2} d x = e^{x} d y

\frac{d y}{d x} = \frac{( 3 x ^{2} - e ^{x} )}{2 y - 5}

\frac{d y}{d x} = \frac{x ^{2}}{cos ( y )}

\frac{d y}{d x} = \frac{( 3 x + 10 ) e ^{- 2 y}}{x ^{2} + 6 x + 8}