JEE Main 2024 Mathematics question
If y = y(x) is the solution curve of the differential equation (x² – 4)dy – (y² – 3y)dx = 0, x > 2, y(4) = 3/2 and the slope of the curve is never zero, then the value of y(10) equals :
Answer: (A)
Solution
dy/(y² − 3y) = dx/(x² − 4) integrates to (1/3)ln|(y − 3)/y| = (1/4)ln|(x − 2)/(x + 2)| + ln C, i.e. |(y − 3)/y|^{1/3}|(x + 2)/(x − 2)|^{1/4} = K. With y(4) = 3/2:
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