If y= h ⁻¹ x 1+x^2 , then (1+x^2 ) y ₂+3 xy ₁+ y =

Step-by-step solution

aligned & Given, y= ⁻¹ x 1+x^2 & 1+x^2 y= ⁻¹ x aligned On differentiating w.r.t. x , we get aligned & 1+x^2 y₁+y 1 2 1+x^2 2 x= 1 1+x^2 & (1+x^2 ) y₁+x y=1 aligned Again, on differentiating w.r.t. x , we get aligned & (1+x^2 ) y₂+y₁ 2 x+x y₁+y=0 & (1+x^2 ) y₂+3 x y₁+y=0 aligned