(dy)/(dx)=((2y+5)^2)/((8x+9)^2)

解

\frac{d y}{d x} = \frac{( 2 y + 5 ) ^{2}}{( 8 x + 9 ) ^{2}}

y = - \frac{16 x}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{160 c _{1} x}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{180 c _{1}}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{31}{2 ( - 1 + 64 c _{1} x + 72 c _{1} )}

解答ステップ

\frac{d y}{d x} = \frac{( 2 y + 5 ) ^{2}}{( 8 x + 9 ) ^{2}}

分離可能 ODE を解く:

y = - \frac{16 x}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{160 c _{1} x}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{180 c _{1}}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{31}{2 ( - 1 + 64 c _{1} x + 72 c _{1} )}

y = - \frac{16 x}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{160 c _{1} x}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{180 c _{1}}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{31}{2 ( - 1 + 64 c _{1} x + 72 c _{1} )}