The differential equation $y^2 d x+(2 x y-1) d y=0$ is
The differential equation $y^2 d x+(2 x y-1) d y=0$ is
linear in $y$
not a linear equation
a homogenous equation
linear in $\mathrm{x}$
Solution
$
\begin{aligned}
& \text {} y^2 d x+(2 x y-1) d y=0 \\
& \Rightarrow \quad \frac{d x}{d y}+\frac{2 x}{y}-\frac{1}{y^2}=0 \\
& \Rightarrow \quad \frac{d x}{d y}+\left(\frac{2}{y}\right) x=\frac{1}{y^2}
\end{aligned}
$
Which of the form $\frac{d x}{d y}+P x=Q$ Hence given equation is linear in $\mathrm{x}$