What is a solution to the differential equation #dy/dx=(1+x)(1+y)#?

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Answer 1 · 2016-07-18T14:47:32

#y =C e^(x + x^2 / 2 ) - 1#

#dy/dx=(1+x)(1+y)#

this is separable!

#1/(1+y) dy/dx=1+x#

so we integrate both sides

#int \ 1/(1+y) dy/dx \ dx=int \ 1+x \ dx#

or

#int \ 1/(1+y) \ dy=int \ 1+x \ dx#

#ln (1+y) = x + x^2 / 2 + C#

#1+y = e^(x + x^2 / 2 + C)#

#y =C e^(x + x^2 / 2 ) - 1#