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QJEEM24Mab49d: JEE Main 2024 Mathematics - Class 12 JEEM24Mab49d Solution: The solution curve, of the differential equation , passing…

The solution curve, of the differential equation 2ydy dx+3=5dy dx2 y \frac{\mathrm{d} y}{\mathrm{~d} x}+3=5 \frac{\mathrm{d} y}{\mathrm{~d} x} , passing through the point (0,1)(0,1) is a conic, whose vertex lies on the line :

Multiple Choice Options

  • A 2x+3y=−92 x+3 y=-9
  • B 2x+3y=−62 x+3 y=-6
  • C 2x+3y=92 x+3 y=9
  • D 2x+3y=62 x+3 y=6

Step-by-Step Verified Solution

amp;2ydydx+3=5dydxamp;2ydy+3dx=5dyamp;y2+3x=5y+c∣(0,1)amp;1+0=5+camp;c=−4amp;y2−5y=−3x−4amp;y2−5y+254−254=−3x−4amp;(y−52)2=−3x+94amp;(y−52)2=−3(x−34)amp;(34,52) satisfies by 2x+3y=9\begin{aligned}& 2 y \frac{d y}{d x}+3=5 \frac{d y}{d x} \\& 2 y d y+3 d x=5 d y \\& y^2+3 x=5 y+\left.c\right|_{(0,1)} \\& 1+0=5+c \\& c=-4 \\& y^2-5 y=-3 x-4 \\& y^2-5 y+\frac{25}{4}-\frac{25}{4}=-3 x-4 \\& \left(y-\frac{5}{2}\right)^2=-3 x+\frac{9}{4} \\& \left(y-\frac{5}{2}\right)^2=-3\left(x-\frac{3}{4}\right) \\& \left(\frac{3}{4}, \frac{5}{2}\right) \text { satisfies by } 2 x+3 y=9\end{aligned}

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