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 \((\mathrm{h}, \mathrm{k})=\)
- A \((1,2)\)
- B \((2,1)\)
- C \((7,8)\)
- D \((8,7)\)
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…
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