Q110 / 160 · AP EAMCET 2015 · Mathematics

The differential equation $\frac{d y}{d x}=\frac{1}{a x+b y+c}$, where $a, b, c$ are all non-zero real numbers, is

  • A
    linear in y
  • Correct answer
    B
    linear in x
  • C
    linear in both x and y
  • D
    homogeneous equation

Solution

Given differential equation, $\begin{aligned} & \frac{d y}{d x}=\frac{1}{a x+b y+c} \\ & \frac{d y}{d x}=a x+b y+c \\ & \frac{d x}{d y}-a x=b y+c \end{aligned}$ Hence, this equation is a linear differential equation in $x$.

Hence, the correct answer is option: 'B'.

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