87544
The differential equation \(\frac{d y}{d x}=\frac{1}{a x+b y+c \text {, }}\) where \(a, b, c\) are all non-zero real numbers, is
1 linear in \(y\)
2 linear in \(\mathrm{x}\)
3 linear in both \(\mathrm{x}\) and \(\mathrm{y}\)
4 homogeneous equation
Explanation:
(B) : Given differential equation- \(\frac{d y}{d x}=\frac{1}{a x+b y+c}\), where a, b, c are non-zero real number, Or \(\quad \begin{aligned} \frac{d y}{d x}=\frac{1}{a x+b y+c} \\ \frac{d x}{d y}=a x+b y+c \\ \frac{d x}{d y}-a x=b y+c\end{aligned}\) Hence, the above equation is a linear differential equation in \(\mathrm{x}\).