TS EAMCET · Maths · Differential Equations
The general solution of \(\frac{d y}{d x}=\frac{x+y+1}{y-x+1}\) is
- A \(2 x y+(x+1)^2-(y+1)^2=C\)
- B \((x+1)^2-(y+1)^2=C+x y\)
- C \((x+1)^2+2 x y=C(y+1)\)
- D \((x+1)(y+1)=C x y\)
Answer & Solution
Correct Answer
(A) \(2 x y+(x+1)^2-(y+1)^2=C\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { We have, } \frac{d y}{d x}=\frac{x+y+1}{y-x+1} \\ & \Rightarrow \quad \begin{aligned} y d y-x d y+d y & =x d x+y d x+d x \\ (y+1) d y & =(x+1) d x+y d x+x d y \\ (y+1) d y & =(x+1) d x+d(x y) \end{aligned} \end{aligned}\) On integrating,…
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