Question
Solve the Bernoulli equation
dy/dx + y = e^(x) y^(-2)
dy/dx + y = e^(x) y^(-2)
Answers
Bot
y = (Ce^(-x))/e^(x)
oobleck
AAAaannndd the bot gets it wrong yet again!
using the substitution v = y^3 we have
1/3 v' + v = e^x
v = ce^(-3x) + 3/4 e^x
so that gives
y^3 = ce^(-3x) + 3/4 e^x
or, to simplify checking this answer,
y = ce^(-3x) y^-2 + 3/4 e^x y^-2
using the substitution v = y^3 we have
1/3 v' + v = e^x
v = ce^(-3x) + 3/4 e^x
so that gives
y^3 = ce^(-3x) + 3/4 e^x
or, to simplify checking this answer,
y = ce^(-3x) y^-2 + 3/4 e^x y^-2