(dy)/(dx)=(((2y+3))/(4x+5))^2

解答

\frac{d y}{d x} = (\frac{( 2 y + 3 )}{4 x + 5})^{2}

y = - \frac{4 x}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{24 c _{1} x}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{30 c _{1}}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{7}{2 ( - 1 + 16 c _{1} x + 20 c _{1} )}

求解步骤

\frac{d y}{d x} = (\frac{( 2 y + 3 )}{4 x + 5})^{2}

求解可分离方程:

y = - \frac{4 x}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{24 c _{1} x}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{30 c _{1}}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{7}{2 ( - 1 + 16 c _{1} x + 20 c _{1} )}

y = - \frac{4 x}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{24 c _{1} x}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{30 c _{1}}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{7}{2 ( - 1 + 16 c _{1} x + 20 c _{1} )}

\frac{d}{d x} (ln (\frac{3 x + 1}{x ^{2} - 2}))

d er i v a t i v e 3 x e^{x} csc (x)

x \to 0 lim (sin^{2} (x) (\frac{1}{x}))

x \to - 1 lim (\frac{1}{x ^{2} + 1})

n = 0 \sum \infty \frac{6}{5 ^{n}}