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  • Please solve RD Sharma class 12 chapter 21 Differential Equation exercise Fill in the blank question 37 maths textbook solution

Please solve RD Sharma class 12 chapter 21 Differential Equation exercise Fill in the blank question 37 maths textbook solution

Answers (1)

Answer:

 \frac{1}{x}

Given:

The integrating factor of differential equation

x\frac{\mathrm{d} y}{\mathrm{d} x}-y=log\, x

is ______

Hint:

 By the help of integrating factor the sum will solve.

Solution:

x\frac{\mathrm{d} y}{\mathrm{d} x}-y=log\, x

\Rightarrow \frac{\mathrm{d} y}{\mathrm{d} x}-\frac{y}{x}=\frac{log\, x}{x}

Comparing the above equation with the standard linear differential equation, we get

\Rightarrow \frac{\mathrm{d} y}{\mathrm{d} x}+Py=Q

Here,

P=\frac{-1}{x}\: and\: Q=\frac{log\, x}{x}

So, integrating factor

e^{\int P\, dx}=e^{\int-\frac{1}{x} dx}=e^{-log\, x}=\frac{1}{x}

So, the answer is

\frac{1}{x}

Posted by

Gurleen Kaur

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