Solve the differential equation (1+x²)dy/dx + y = etan⁻¹x

(1+x²)dy/dx+y=etan⁻¹x
dy/dx+y/(1+x²)=etan⁻¹x/(1+x²)
It is linear differential equation of first order.
Comparing with standard linear differential equation.
dy/dx+P(x)y=Q(x)
P(x)=1/(1+x²);Q(x)=etan⁻¹x/(1+x²)
Integrating factor(IF) =e∫Pdx=e∫1/(1+x²)dx=etan⁻¹x
Solution of LDE, y.IF=∫IFQ(x)dx+C
y.etan⁻¹x=∫etan⁻¹x.etan⁻¹x/(1+x²)dx+C
y.etan⁻¹x=∫(etan⁻¹x)²/(1+x²)dx+C—(1)
To solving ∫(etan⁻¹x)²/(1+x²)dx
Put etan⁻¹x=t
etan⁻¹x.(1/(1+x²))dx=dt
Therefore, ∫etan⁻¹x.etan⁻¹x/(1+x²)dx=∫tdt=t²/2+C
⇒(etan⁻¹x)²/2+C
Substituting in (1),
y.etan⁻¹x=(etan⁻¹x)²/2+C