defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Differential Equations Solution of Differential Equations
The solution curve of the differential equation \(\rm y\frac{dx}{dy}=x(\log_e x-\log_e y+1), x >0, y>0\) passing through the point (e, 1) is
1
\(\rm \left|\log_e\frac{y}{x}\right|=x\)
2
\(\rm \left|\log_e\frac{y}{x}\right|=y^2\)
3
\(\rm \left|\log_e\frac{x}{y}\right|=y\)
4
\(\rm 2\left|\log_e\frac{x}{y}\right|=y+1\)