The solution of the differential equation d y d x = x-y x is ....… - Vidyadip

MCQ

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

✓
$y \sec x=\tan x+ c$
B
$y \sec x+\tan x=c$
C
$\sec x=y \tan x+c$
D
$\sec x+y \tan x=c$

✓

Answer

Correct option: A.

$y \sec x=\tan x+ c$

(A)
$\frac{d y}{d x}+y \tan x=\sec x$
The given equation is of the form
$\frac{d y}{d x}+P y=Q$
I. $f==e^{\int P d x}=e^{\int \tan x d x}$
$\begin{aligned} & =e^{\log |\sec x|} \\ & =\sec x\end{aligned}$
Solution of the given equation is
$\begin{aligned} & y \cdot(I \cdot F)=\int Q(I \cdot F) d x+c \\ & y \sec x=\int \sec x \sec x d x+c \\ & y \sec x=\tan x+c\end{aligned}$

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