AP EAMCET · Maths · Differential Equations
The solution of the differential equation \((2 x-4 y+3) \frac{d y}{d x}+(x-2 y+1)=0\) is
( \(C\) is an arbitrary constant)
- A \(\log [(2 x-4 y)+3]=x-2 y+C\)
- B \(\log [2(2 x-4 y)+3]=2(x-2 y)+C\)
- C \(\log [2(x-2 y)+5]=2(x+y)+C\)
- D \(\log [4(x-2 y)+5]=4(x+2 y)+C\)
Answer & Solution
Correct Answer
(D) \(\log [4(x-2 y)+5]=4(x+2 y)+C\)
Step-by-step Solution
Detailed explanation
Given differential equation, \(\begin{aligned} & (2 x-4 y+3) \frac{d y}{d x}+(x-2 y+1)=0 \\ & \Rightarrow \quad \frac{d y}{d x}=\frac{(x-2 y+1)}{2(x-2 y+3)} \quad \ldots \text { (i) } \end{aligned}\) Let, \(x-2 y=v \Rightarrow 1-2 \frac{d y}{d x}=\frac{d y}{d x}\)…
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