Question

Bernoulli equation:(1+x^2)y'+2xy=1/(1+x^2)

Answer 1

any one know the ans?

Answer 2

\[y'+\frac{ 2x }{ 1+x^2 }y=\frac{ 1 }{ \left( 1+x^2 \right) ^2}\]
i.f=\[e ^{\int\limits \frac{ 2x }{ 1+x^2 }dx}=e ^{\ln \left( 1+x^2 \right)}=1+x^2\]

Answer 3

c.s. is
\[y \left( 1+x^2 \right)=\int\limits \frac{ 1 }{ \left( 1+x^2 \right)^2 }\left( 1+x^2 \right)dx+c\]
you know how to complete it.

Answer 4

\[y \left( 1+x^2 \right)=\int\limits \frac{ 1 }{ 1+x^2 }dx+c\]
\[\int\limits \frac{ 1 }{ 1+x^2 }dx=\tan^{-1} x\]