(e^y+21)^2e^{-y}dx+(e^x+1)^3e^{-x}dy=0

解

(e^{y} + 21)^{2} e^{- y} d x + (e^{x} + 1)^{3} e^{- x} d y = 0

y = ln (- \frac{2 ( e ^{x} + 1 ) ^{2}}{1 + 2 c _{1} ( e ^{x} + 1 ) ^{2}} - \frac{42 c _{1} ( e ^{x} + 1 ) ^{2}}{1 + 2 c _{1} ( e ^{x} + 1 ) ^{2}} - \frac{21}{1 + 2 c _{1} ( e ^{x} + 1 ) ^{2}})

解答ステップ

(e^{y} + 21)^{2} e^{- y} d x + (e^{x} + 1)^{3} e^{- x} d y = 0

分離可能 ODE を解く:

y = ln (- \frac{2 ( e ^{x} + 1 ) ^{2}}{1 + 2 c _{1} ( e ^{x} + 1 ) ^{2}} - \frac{42 c _{1} ( e ^{x} + 1 ) ^{2}}{1 + 2 c _{1} ( e ^{x} + 1 ) ^{2}} - \frac{21}{1 + 2 c _{1} ( e ^{x} + 1 ) ^{2}})

y = ln (- \frac{2 ( e ^{x} + 1 ) ^{2}}{1 + 2 c _{1} ( e ^{x} + 1 ) ^{2}} - \frac{42 c _{1} ( e ^{x} + 1 ) ^{2}}{1 + 2 c _{1} ( e ^{x} + 1 ) ^{2}} - \frac{21}{1 + 2 c _{1} ( e ^{x} + 1 ) ^{2}})