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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ri1men4dp

Answered 2022-07-27
Author has **14** answers

y=cx-2

y'=c

xy'=cx=y+2.

y=cx-2

3=c-2

c=5.

y'=c

xy'=cx=y+2.

y=cx-2

3=c-2

c=5.

Shannon Andrews

Answered 2022-07-28
Author has **5** answers

The differential equation can be separated: dy/(y+2)=dx/x.Integration: $\mathrm{ln}(y+2)=\mathrm{ln}(cx)$. Exponentiated: y+2=cx. So y=cx-2 is shown. $\int dx/x=\mathrm{ln}(x)+C=\mathrm{ln}(x)+\mathrm{ln}(\mathrm{exp}(C))=\mathrm{ln}(x\mathrm{exp}(C))=\mathrm{ln}(cx)$.y(1)=3=3c-2 is solved by c=5/3. y(x)=5x/3-2.

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