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GUJCET · Maths · Differential Equations
The particular solution of the differential equation \(\frac{d y}{d x}=-4 x y^2\) with initial condition \(x=0, y=1\) is ____________ .
- A \(y=\frac{x}{2 x^2+1}\)
- B \(y=\frac{1}{2 x^2+1}\)
- C \(y=2 x^2+1\)
- D \(x=\frac{1}{2 y^2+1}\)
Answer & Solution
Correct Answer
(B) \(y=\frac{1}{2 x^2+1}\)
Step-by-step Solution
Detailed explanation
\(\int \frac{dy}{y^2} = \int -4x \,dx\) \(-\frac{1}{y} = -2x^2 + C\)
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