The solution of the differential equation dydx+2xy1+x2=11+x22 is
y(1-x2)=tan-1x+c
y(1+x2)=tan-1x+c
y(1+x2)2=tan-1x+c
y(1-x2)2=tan-1x+c
Explanation for the correct option
Given: dydx+2xy1+x2=11+x22
Let P=2x1+x2and Q=11+x22
Integrating factor I=e∫Pdx
I=e∫2x1+x2dx⇒I=elog(1+x2)∫f'(x)f(x)dx=log(f(x))⇒I=1+x2elog(x)=x
general solution=1I∫I·Q·dx
⇒y=11+x2∫1+x211+x22·dx⇒y=11+x2∫11+x2·dx∫11+a2·da=tan-1(a)+c⇒y(1+x2)=tan-1(x)+c
Hence, option B is correct.
The solution of the differential equation dydx=1+y21+x2 is
[SCRA 1986]