WBJEE · Maths · Differential Equations
The general solution of the differential equation \(\frac{d y}{d x}=\frac{x+y+1}{2 x+2 y+1}\) is
- A \(\log _{e}|3 x+3 y+2|+3 x+6 y=C\)
- B \(\log _{e}|3 x+3 y+2|-3 x+6 y=C\)
- C \(\log _{e}|3 x+3 y+2|-3 x-6 y=C\)
- D \(\log _{e}|3 x+3 y+2|+3 x-6 y=C\)
Answer & Solution
Correct Answer
(D) \(\log _{e}|3 x+3 y+2|+3 x-6 y=C\)
Step-by-step Solution
Detailed explanation
Given differential equation, \(\frac{d y}{d x}=\frac{x+y+1}{2 x+2 y+1}\) Put \(x+y=v\) \(\Rightarrow \quad 1+\frac{d y}{d x}=\frac{d v}{d x} \Rightarrow \frac{d y}{d x}=\frac{d v}{d x}-1\) \(\therefore\) Eq. (i) becomes, \(\frac{d y}{d x}=\frac{v+1}{2 v+1}\)…
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