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  • Explain solution RD Sharma class 12 Chapter 21 Differential Equation exercise 21.10 question 17

Explain solution RD Sharma class 12 Chapter 21 Differential Equation exercise 21.10 question 17

Answers (1)

Answer:  y \sec x=x+C

Hint: To solve this equation we use  e\int P dx  formula.

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

Solution:  \frac{d y}{d x}+P y=Q

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

\text { If }=e^{\int P d x} \\

=e^{\int \tan x d x} \\

=e^{\log \sec x} \\

=\sec x

\begin{aligned} &=y I f=\int Q I f d x+C \\ &=y \sec x=\int \sec x \cos x d x \\ &=y \sec x=\int \frac{1}{\cos x} \cos x d x \\ &=y \sec x=\int 1 d x \\ &=y \sec x=x+C \end{aligned}

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