TS EAMCET · Maths · Differential Equations
The general solution of the differential equation \((3 y-7 x+7) d x+(7 y-3 x+3) d y=0\) is
- A \((x-y+1)^2(x+y-1)^5=C\)
- B \((x+y+1)^5(x-y-1)^2=C\)
- C \((x-y-1)^2(x+y-1)^5=C\)
- D \((x+y-1)^7=C\)
Answer & Solution
Correct Answer
(C) \((x-y-1)^2(x+y-1)^5=C\)
Step-by-step Solution
Detailed explanation
We have, \((3 y-7 x+7) d x+(7 y-3 x+3) d y=0\) \(\Rightarrow(7 x-3 y-7) d x+(3 x-7 y-3) d y=0\) \(\ldots(\mathrm{i})\) Given equation is non-homogeneous and \(a_1 b_2-a_2 b_1=-40 \neq 0\) On solving \(7 x-3 y-7=0\) and \(3 x-7 y-3=0\) we get \(x=1, y=0\) Now, substitude…
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