d/(df)(\H(f))=(1+u(f)^2)/(1+f^2)

解

\frac{d}{df} (H (f)) = \frac{1 + u ( f ) ^{2}}{1 + f ^{2}}

u (f) = \frac{c _{1}}{e ^{a r c t a n (f) - f}} - \frac{\int - \frac{e ^{- f + a r c t a n (f)}}{1 + f ^{2}} df}{e ^{a r c t a n (f) - f}}

解答ステップ

\frac{d}{df} (H (f)) = \frac{1 + u ( f ) f ^{2}}{1 + f ^{2}}

完全 ODE を解く:

u (f) = \frac{c _{1}}{e ^{a r c t a n (f) - f}} - \frac{\int - \frac{e ^{- f + a r c t a n (f)}}{1 + f ^{2}} df}{e ^{a r c t a n (f) - f}}

u (f) = \frac{c _{1}}{e ^{a r c t a n (f) - f}} - \frac{\int - \frac{e ^{- f + a r c t a n (f)}}{1 + f ^{2}} df}{e ^{a r c t a n (f) - f}}