defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Differential Equations Solution of Differential Equations
Let y = y(x) be the solution of the differential equation \(\rm \frac{dy}{dx}\) = 2x (x + y)3 – x (x + y) – 1, y(0) = 1. Then, \(\rm\left(\frac{1}{\sqrt2}+y\left(\frac{1}{\sqrt2}\right)\right)^2\) equals :
1
\(\rm \frac{4}{4+\sqrt e}\)
2
\(\rm \frac{3}{3-\sqrt e}\)
3
\(\rm \frac{2}{1+\sqrt e}\)
4
\(\rm \frac{1}{2-\sqrt e}\)