WBJEE · Maths · Differentiation
If \(y=e^{\tan ^{-1} x}\) then
- A \(\left(1+x^2\right) y_2+(2 x-1) y_1=0\)
- B \(\left(1+x^2\right) y_2+2 x y=0\)
- C \(\left(1+x^2\right) y_2-y_1=0\)
- D \(\left(1+x^2\right) y_2+3 x y_1+4 y=0\)
Answer & Solution
Correct Answer
(A) \(\left(1+x^2\right) y_2+(2 x-1) y_1=0\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=e^{\tan ^{-1} x} \times \frac{1}{1+x^2}\) \(\Rightarrow\left(1+x^2\right) y^{\prime}=y\) or \(2 x y^{\prime}+\left(1+x^2\right) y^{\prime \prime}=y^{\prime}\) or \(\left(1+x^2\right) y^{\prime \prime}+y^{\prime}(2 x-1)=0\)
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