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Need solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise 21.10 Question 17 textbook solution.

Answers (1)

Answer : $y\sec x = x+c$

Hint : To solve this equation we use $e^{\int P d x}$ formula.

Give : $\frac{d y}{d x}+y \tan x=\cos x$

Solution : $\frac{d y}{d x}+Py=Q$

$\begin{aligned} &P=\tan x, Q=\cos x \\ \end{aligned}$

$\begin{aligned} &I f=e^{\int P d x} \\ \end{aligned}$

$\begin{aligned} &=e^{\int \tan x d x} \\ \end{aligned}$

$\begin{aligned} &=e^{\log \sec x} \\ \end{aligned}$

$\begin{aligned} &=\sec x \\ \end{aligned}$

$\begin{aligned} &=y I f=\int Q I f d x+C \\ \end{aligned}$

$\begin{aligned} &=y \sec x=\int \sec x \cos x d x \\ \end{aligned}$

$\begin{aligned} &=y \sec x=\int \frac{1}{\cos x} \cos x d x \\ \end{aligned}$

$\begin{aligned} &=y \sec x=\int 1 d x \\ \end{aligned}$

$\begin{aligned} &=y \sec x=x+C \end{aligned}$

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