JEE Mains · Maths · STD 12 - 9. differential equations
Let slope of the tangent line to a curve at any point \(P ( x , y )\) be given by \(\frac{ xy ^{2}+ y }{ x } .\) If the curve intersects the line \(x+2 y=4\) at \(x=-2,\) then the value of \(y ,\) for which the point \((3, y )\) lies on the curve, is ..... .
- A \(\frac{18}{35}\)
- B \(-\frac{4}{3}\)
- C \(-\frac{18}{19}\)
- D \(-\frac{18}{11}\)
Answer & Solution
Correct Answer
(C) \(-\frac{18}{19}\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=\frac{x y^{2}+y}{x}\) \(\frac{x d y-y d x}{y^{2}}=x d x\) \(-d\left(\frac{x}{y}\right)=x d x\) \(-\frac{x}{y}=\frac{x^{2}}{2}+c\) \(\because\) curve intersects the line \(x+2 y=4\) at \(x =-2 \Rightarrow\) point of intersection is (-2,3) \(\therefore\) curve…
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