Solve and classify equation dy/dx= - (e^x+y)/(k+x+ye^x), y(0)=1

Jerold 2020-11-14 Answered
Solve and classify equation dy/dx=(ex+y)/(k+x+yex), y(0)=1
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Expert Answer

Alix Ortiz
Answered 2020-11-15 Author has 109 answers
Solving the numerator part and denominator part
According the first order linear differential equation
ex+y
y=yy=ex
y=exx+c1ex
Solving the denominator part through first order linear differential equation
dy/dx=k+x+yex
y=k+x+yex
yexy=k+x
solving the parts
y=(exx+c1ex)/((k+x)/ex)
This equation is in homogeneous form
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