The differential equation of all lines perpendicular to the line $5 x+2 y+7=0$ is
The differential equation of all lines perpendicular to the line $5 x+2 y+7=0$ is
3dy-2dx=0
2dy-5dx=0
2dy-3dx=0
5dy-2dx=0
Solution
Given line $5 x+2 y+7=0$ has slope $\frac{-5}{2}$. Hence eq. of required line is
$\begin{aligned}
& y=\frac{2}{5} x+c \Rightarrow 2 x-5 y+c=0 \\
\therefore & 2-5 \frac{d y}{d x}=0 \Rightarrow 2=5 \frac{d y}{d x} \Rightarrow 2 d x=5 d y \Rightarrow 5 d y-2 d x=0
\end{aligned}$