MHT CET · Maths · Differential Equations
The differential equation of all lines perpendicular to the line \(5 x+2 y+7=0\) is
- A 3dy-2dx=0
- B 2dy-5dx=0
- C 2dy-3dx=0
- D 5dy-2dx=0
Answer & Solution
Correct Answer
(D) 5dy-2dx=0
Step-by-step Solution
Detailed explanation
(C)
Given line \(5 x+2 y+7=0\) has slope \(\frac{-5}{2}\). Hence eq. of required line is
\(y=\frac{2}{5} x+c \Rightarrow 2 x-5 y+c=0\)
\(\therefore 2-5 \frac{d y}{d x}=0 \Rightarrow 2=5 \frac{d y}{d x} \Rightarrow 2 d x=5 d y \Rightarrow\) \(5 d y-2 d x=0\)
Given line \(5 x+2 y+7=0\) has slope \(\frac{-5}{2}\). Hence eq. of required line is
\(y=\frac{2}{5} x+c \Rightarrow 2 x-5 y+c=0\)
\(\therefore 2-5 \frac{d y}{d x}=0 \Rightarrow 2=5 \frac{d y}{d x} \Rightarrow 2 d x=5 d y \Rightarrow\) \(5 d y-2 d x=0\)
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