y=((x+1)^3)/(x^{3/2)}(dy)/(dx)

解答

y = \frac{( x + 1 ) ^{3}}{x ^{\frac{3}{2}}} \frac{d y}{d x}

y = e^{c_{1} + \frac{- 5 x ^{\frac{3}{2}} - 3 x ^{\frac{1}{2}} + 3 x ^{2} a r c t a n ( x ^{\frac{1}{2}} ) + 6 x a r c t a n ( x ^{\frac{1}{2}} ) + 3 a r c t a n ( x ^{\frac{1}{2}} )}{4 ( x + 1 ) ^{2}}}

求解步骤

y = \frac{( x + 1 ) ^{3}}{x ^{\frac{3}{2}}} \frac{d y}{d x}

求解可分离方程:

y = e^{c_{1} + \frac{- 5 x ^{\frac{3}{2}} - 3 x ^{\frac{1}{2}} + 3 x ^{2} a r c t a n ( x ^{\frac{1}{2}} ) + 6 x a r c t a n ( x ^{\frac{1}{2}} ) + 3 a r c t a n ( x ^{\frac{1}{2}} )}{4 ( x + 1 ) ^{2}}}

y = e^{c_{1} + \frac{- 5 x ^{\frac{3}{2}} - 3 x ^{\frac{1}{2}} + 3 x ^{2} a r c t a n ( x ^{\frac{1}{2}} ) + 6 x a r c t a n ( x ^{\frac{1}{2}} ) + 3 a r c t a n ( x ^{\frac{1}{2}} )}{4 ( x + 1 ) ^{2}}}

y^{^{'}} = y^{3} e^{- x}

\frac{d V}{d t} = 20 - \frac{5}{100} V, V (0) = 0

y^{^{'}} = x \cdot y - x - 2 \cdot y + 2

(1 + x^{4}) d y + x (1 + 4 y^{2}) d x = 0, y (1) = 1

\frac{d x}{d t} = 12 \cdot x \cdot t