JEE Mains · Maths · STD 12 - 9. differential equations
The solution curve, of the differential equation \(2 \mathrm{y} \frac{\mathrm{dy}}{\mathrm{dx}}+3=5 \frac{\mathrm{dy}}{\mathrm{dx}}\), passing through the point \((0,1)\) is a conic, whose vertex lies on the line :
- A \(2 x+3 y=9\)
- B \(2 x+3 y=-9\)
- C \(2 x+3 y=-6\)
- D \(2 x+3 y=6\)
Answer & Solution
Correct Answer
(A) \(2 x+3 y=9\)
Step-by-step Solution
Detailed explanation
\( (2 y-5) \frac{d y}{d x}=-3 \) \( (2 y-5) d y=-3 d x \) \( 2 \cdot \frac{y^2}{2}-5 y=-3 x+\lambda\) \(\because\) Curve passes through \((0,1)\) \(\Rightarrow \lambda=-4\) \(\because\) Curve will be \(\left(y-\frac{5}{2}\right)^2=-3\left(x-\frac{3}{4}\right)\) \(\therefore\)…
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