解
(ey+1)2e−ydx+(ex+1)3dy=0
解
y=ln(2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32xex2−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32ln(ex+1)ex2−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32c1ex2−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32ex2+2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−34xex−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−34ln(ex+1)ex−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−34c1ex−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32ex−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32ln(ex+1)+2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32x+2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−31−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32c1)
解答ステップ
(ey+1)2e−ydx+(ex+1)3dy=0
分離可能 ODE を解く:y=ln(2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32xex2−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32ln(ex+1)ex2−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32c1ex2−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32ex2+2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−34xex−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−34ln(ex+1)ex−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−34c1ex−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32ex−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32ln(ex+1)+2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32x+2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−31−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32c1)
y=ln(2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32xex2−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32ln(ex+1)ex2−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32c1ex2−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32ex2+2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−34xex−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−34ln(ex+1)ex−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−34c1ex−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32ex−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32ln(ex+1)+2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32x+2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−31−2c1+2ln(1+ex)+2ln(1+ex)ex2+2c1ex2+4ln(1+ex)ex+4c1ex−2x−2xex2−2ex−4xex−32c1)