Q119 / 160 · TS EAMCET 2008 · Mathematics

The solution of the differential equation $\frac{d y}{d x}-y \tan x=e^x \sec x$ is

  • A
    $y=e^x \cos x+c$
  • Correct answer
    B
    $y \cos x=e^x+c$
  • C
    $y=e^x \sin x+c$
  • D
    $y \sin x=e^x+c$

Solution

Given linear differential equation is $$ \begin{aligned} \frac{d y}{d x}-y \tan x & =e^x \sec x \\ \therefore \quad \quad \quad \mathrm{IF}=e^{\int-\tan x d x} & =e^{-\log \sec x} \\ & =\frac{1}{\sec x} \end{aligned} $$ $\therefore$ Complete solution is $$ \begin{array}{rlrl} & & y \cdot \frac{1}{\sec x} & =\int e^x \sec x \cdot \frac{1}{\sec x} d x \\ \Rightarrow & & \frac{y}{\sec x} & =e^x+c \\ \Rightarrow & y \cos x & =e^x+c \end{array} $$

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

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