What is a solution to the differential equation \frac{dy}{dx}=(1+x)(1+y)?

Papierskiix5n

Papierskiix5n

Answered question

2022-04-16

What is a solution to the differential equation dydx=(1+x)(1+y)?

Answer & Explanation

tempur8x43

tempur8x43

Beginner2022-04-17Added 16 answers

dydx=(1+x)(1+y)
this is separable!
11+ydydx=1+x
so we integrate both sides
11+ydydxdx=1+xdx
or
11+ydy=1+xdx
ln(1+y)=x+x22+C
1+y=ex+x22+C
y=Cex+x221

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