AP EAMCET · Maths · Differential Equations
Find the particular solution of the following differential equation, given that \(y=1\), when \(x=0,\left(1+x^2\right) \frac{d y}{d x}=e^{m\left(\tan ^{-1} x\right)}-y\)
- A \(x e^{\tan ^{-1}(x)}=\tan ^{-1}(x)+1\)
- B \(x e^{\tan ^{-1}(x)}=\tan ^{-1}(x)-1\)
- C \(y e^{\tan ^{-1}(x)}=\tan ^{-1}(x)+1\)
- D \(y e^{\tan ^{-1}(x)}=\tan ^{-1}(x)-1\)
Answer & Solution
Correct Answer
(C) \(y e^{\tan ^{-1}(x)}=\tan ^{-1}(x)+1\)
Step-by-step Solution
Detailed explanation
Given, differential equation \(\left(1+x^2\right) \frac{d y}{d x}=e^{m\left(\tan ^{-1} x\right)}-y, y(0)=1\) \(\frac{d y}{d x}=\frac{e^{m \tan ^{-1} x}}{1+x^2}-\frac{y}{1+x^2}\) \(\Rightarrow \quad \frac{d y}{d x}+y\left(\frac{1}{1+x^2}\right)=\frac{e^{m \tan ^{-1} x}}{1+x^2}\)…
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