Is x=0 a peculiar solution?

[evinda]

Hi!!
I have a question..Given the differential equation \(\displaystyle xy'+6y=3xy^{\frac{4}{3}}\),I found that \(\displaystyle y(x)=\frac{1}{(x+cx^{2})^{3}}, x\in(-\infty,+\infty)-\{0,\frac{-1}{c}\}\).But..is \(\displaystyle x=0\) a peculiar solution?

 

[Deleted member 4993]

Hi!!
I have a question..Given the differential equation \(\displaystyle xy'+6y=3xy^{\frac{4}{3}}\),I found that \(\displaystyle y(x)=\frac{1}{(x+cx^{2})^{3}}, x\in(-\infty,+\infty)-\{0,\frac{-1}{c}\}\).But..is \(\displaystyle x=0\) a peculiar solution?

As I interpret the answer \(\displaystyle y(x)=\frac{1}{(x+cx^{2})^{3}}, x\in(-\infty,+\infty)-\{0,\frac{-1}{c}\}\)

means

\(\displaystyle y(x)=\frac{1}{(x+cx^{2})^{3}}, x\in(-\infty,+\infty)\) except at x = 0 and x = -1/c

so x= 0 is not included in your solution set.

 

[evinda]

As interpret the answer \(\displaystyle y(x)=\frac{1}{(x+cx^{2})^{3}}, x\in(-\infty,+\infty)-\{0,\frac{-1}{c}\}\)

means

\(\displaystyle y(x)=\frac{1}{(x+cx^{2})^{3}}, x\in(-\infty,+\infty)\) except at x = 0 and x = -1/c

so x= 0 is not included in your solution set.

So,it is not a peculiar solution,right?

 

[stapel]

is \(\displaystyle x=0\) a peculiar solution?

By "peculiar", do you perhaps mean "particular"? Thank you!