JEE Mains · Maths · STD 12 - 9. differential equations
If the curve, \(y = y ( x )\) represented by the solution of the differential equation \(\left(2 x y^{2}-y\right) d x+x d y=0,\) passes through the intersection of the lines, \(2 x -3 y =1\) and \(3 x+2 y=8,\) then \(|y(1)|\) is equal to ...... .
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\(\left(2 x y^{2}-y\right) d x+x d y=0\) \(2 x y^{2} d x-y d x+x d y=0\) \(2 x dx =\frac{ y d x - x dy }{ y ^{2}}= d \left(\frac{ x }{ y }\right)\) Now integrate \(x ^{2}=\frac{ x }{ y }+ c\) Now point of intersection of lines are \((2,1)\)…
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