Q81 / 160 · AP EAMCET 2020 (21 Sep Shift 2) · Mathematics

The general solution of the differential equation \(\log \left(\frac{d y}{a x}\right)=a x+b y\) is

  • Correct answer
    A
    \(a e^{-b y}+b e^{a x}=c\)
  • B
    \(a e^{a x}+b e^{-b y}=c\)
  • C
    \(a e^{-b y}-b e^{a x}=c\)
  • D
    \(a e^{b y}+b e^{-a x}=c\)

Solution

Given differential equation \(\begin{array}{llll} & \log \left(\frac{d y}{d x}\right) =a x+b y \\ \Rightarrow & \frac{d y}{d x}=e^{a x+b y} =e^{a x} \cdot e^{b y} \\ \Rightarrow & \int e^{-b y} d y =\int e^{a x} d x \Rightarrow-\frac{1}{b} e^{-b y}=\frac{1}{a} e^{a x}+c^1 \\ \Rightarrow & b e^{a x}+a e^{-b y} =c \end{array}\) Hence, option (a) is correct.

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

Relevant Questions