sqrt(y)dx+(x-1)dy=0,y(2)=9

解答

y d x + (x - 1) d y = 0, y (2) = 9

y = \frac{ln ^{2} ( x - 1 )}{4} - \frac{c _{1} ln ( x - 1 )}{2} + \frac{c _{1}^{2}}{4}

求解步骤

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

求解可分离方程:

y = \frac{ln ^{2} ( x - 1 )}{4} - \frac{c _{1} ln ( x - 1 )}{2} + \frac{c _{1}^{2}}{4}

y = \frac{ln ^{2} ( x - 1 )}{4} - \frac{c _{1} ln ( x - 1 )}{2} + \frac{c _{1}^{2}}{4}

d er i v a t i v e y = \frac{x ^{2} + 8 x + 3}{x}

\frac{d}{d x} (\frac{g ( x ) ( x )}{a x ^{2} + x})

t an g e n t \frac{7}{x ^{2} + 3}

\frac{d}{d x} (x^{2} sin (x) + 2 x cos (x))

\frac{d y}{d x} = \frac{2 y}{2 x + 1}, y (0) = e