COMEDK · Maths · 32. Differential Equations
The differential equation of the family of straight lines whose slope is equal to \(y\)-intercept is
- A \((x+1) \frac{d y}{d x}+y=0\)
- B \((x+1) \frac{d y}{d x}-y=0\)
- C \(\frac{d y}{d x}=\frac{x+1}{y+1}\)
- D \(\frac{d y}{d x}=\frac{x-1}{y-1}\)
Answer & Solution
Correct Answer
(B) \((x+1) \frac{d y}{d x}-y=0\)
Step-by-step Solution
Detailed explanation
We have, equation of line is \[ y=m x+C \] But \(m=C\) (given) \[ \therefore \quad y=C x+C \] \(\operatorname{Now}, \frac{d y}{d x}=C\) \[ \therefore \quad y=\frac{d y}{d x}(x+1) \Rightarrow(x+1) \frac{d y}{d x}-y=0 \] which is required differential equation.
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