AP EAMCET · Maths · Differential Equations
The general solution of the differential equation \((x-y-1) d y=(x+y+1) d x\) is
- A \(\tan ^{-1}\left(\frac{y+1}{x}\right)-\frac{1}{2} \log \left(x^2+y^2+2 y+1\right)=c\)
- B \((x-y)+\log (x+y)=c\)
- C \(y^2-x^2+x y-3 y-x=c\)
- D \((x-y-1)^2(x+y+1)^3=c\)
Answer & Solution
Correct Answer
(A) \(\tan ^{-1}\left(\frac{y+1}{x}\right)-\frac{1}{2} \log \left(x^2+y^2+2 y+1\right)=c\)
Step-by-step Solution
Detailed explanation
Given differential equation \(\frac{d y}{d x}=\frac{x+y+1}{x-y-1}\) \(\begin{aligned} & \text { Let } \mathrm{x}=X+h, y=Y+k \Rightarrow \frac{d y}{d x}=\frac{d Y}{d X} \\ & \Rightarrow \frac{d Y}{d X}=\frac{X+Y+h+k+1}{X-Y+h-k-1}\end{aligned}\) Since, \(h+k+1=0\) \(h-k-1=0\)…
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