Solution of the differential equation \,f(x)f'(x)+f'(x) = g(x)? How do we

znacimavjo

znacimavjo

Answered question

2022-04-23

Solution of the differential equation ,f(x)f(x)+f(x)=g(x)?
How do we solve a differential equation of the form
f(x)f(x)+f(x)=g(x)?
The coefficient f(x) of f'(x) post a difficulty that integrating factors doesn't work.

Answer & Explanation

potomakavkl

potomakavkl

Beginner2022-04-24Added 11 answers

Step 1
g(x)=f(x)f(x)+f(x)=(f2(x)2+f(x))
and hence, if G(x)=g(x),dx, then
Step 2
f2(x)2+f(x)=G(x)+c
and thus big(f(x)+1big)2=f2(x)+2f(x)+1=2G(x)+2c+1
Therefore f(x)=±2G(x)+c~1

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