Show that y= cx - 2 is a general solution of xy'=y+ 2, where c is an arbitrary constant and find c if y(1)=3

Matilda Fox 2022-07-26 Answered
Show that y= cx - 2 is a general solution of xy'=y+ 2, where c isan arbitrary constant and find c if y(1)=3
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Answers (2)

ri1men4dp
Answered 2022-07-27 Author has 14 answers
Shannon Andrews
Answered 2022-07-28 Author has 5 answers
The differential equation can be separated: dy/(y+2)=dx/x.Integration: ln ( y + 2 ) = ln ( c x ). Exponentiated: y+2=cx. So y=cx-2 is shown. d x / x = ln ( x ) + C = ln ( x ) + ln ( exp ( C ) ) = ln ( x exp ( C ) ) = ln ( c x ).y(1)=3=3c-2 is solved by c=5/3. y(x)=5x/3-2.
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