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AP EAMCET · Maths · Differential Equations

The equation of the curve passing through the point \((0, \pi)\) and satisfying the differential equation \(y d x=\left(x+y^3 \cos y\right) d y\) is

  1. A \(x=y^2 \sin y+y \cos ^2 y\)
  2. B \(x=y^2 \sin y+2 y \cos ^2 \frac{y}{2}\)
  3. C \(x=y^2 \sin y+y \cos ^2 \frac{y}{2}\)
  4. D \(x=y^2 \sin y-y \cos ^2 y\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(x=y^2 \sin y+2 y \cos ^2 \frac{y}{2}\)

Step-by-step Solution

Detailed explanation

\(\frac{dx}{dy} - \frac{1}{y} x = y^2 \cos y\) \(IF = e^{\int -\frac{1}{y} dy} = \frac{1}{y}\) \(\frac{x}{y} = \int y \cos y dy = y \sin y + \cos y + C\) \(x = y^2 \sin y + y \cos y + Cy\)…