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AP EAMCET · Maths · Differential Equations

If \(X=x+h, Y=y+k\) transforms \(\frac{d y}{d x}=\frac{2 x+3 y-7}{3 x+2 y-8}\) to a homogeneous differential equation, then \((\mathrm{h}, \mathrm{k})=\)

  1. A \((1,2)\)
  2. B \((2,1)\)
  3. C \((7,8)\)
  4. D \((8,7)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \((2,1)\)

Step-by-step Solution

Detailed explanation

\(\because \frac{d y}{d x}=\frac{2 x+3 y-7}{3 x+2 y-8}\) ...(i) Let us use the transformation : \(\begin{aligned} & X=x+h \Rightarrow x=X-h \\ & Y=y+k \Rightarrow y=Y-k \\ & \text { And } \frac{d X}{d Y}=\frac{d x}{d y}\end{aligned}\) Using above transformation in eq (i), we get…