defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Differential Equations Formation of a Differential Equation
If x = a(cos θ + θ sin θ), y = a(sin θ - θ cos θ), then at \(\theta = \frac{\pi }{4}\), we have
1
\(\frac{{dy}}{{dx}} = 1\)
2
\(\frac{{{d^2}y}}{{d{x^2}}} = \frac{{8\sqrt 2 }}{{a\pi }}\)
3
\(\frac{{dy}}{{dx}} = - 1\)
4
\(\frac{{{d^2}y}}{{d{x^2}}} = \frac{{ - 8\sqrt 2 }}{{a\pi }}\)