Solution
(ey+1)2e−ydx+(ex+1)3dy=0
Solution
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)
Solution steps
(ey+1)2e−ydx+(ex+1)3dy=0
Solve separable ODE: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)
Graph
Popular Examples
integral of 4e^x+12x^3+4xtangent of f(x)=2sin(x),\at x= pi/4slope of (5.2)(-9.6)derivative of e^{x^2-x}slope of y=3+4x^2-2x^3x=a
Frequently Asked Questions (FAQ)
What is the solution for (e^y+1)^2e^{-y}dx+(e^x+1)^3dy=0 ?
The solution for (e^y+1)^2e^{-y}dx+(e^x+1)^3dy=0 is