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  • Please solve RD Sharma class 12 chapter 21 Differential Equation exercise Fill in the blank question 17 maths textbook solution

Please solve RD Sharma class 12 chapter 21 Differential Equation exercise Fill in the blank question 17 maths textbook solution

Answers (1)

Answer:

 \frac{e^{x}}{x}

Hint:

 Use the form

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

to find the integrating factor.

Given:

 \frac{\mathrm{d} y}{\mathrm{d} x}+y=\frac{1+y}{x}

Solution:

\frac{\mathrm{d} y}{\mathrm{d} x}+y-\frac{y}{x}=\frac{1}{x}

\Rightarrow \frac{\mathrm{d} y}{\mathrm{d} x}+y\left ( 1-\frac{1}{x} \right )=\frac{1}{x}

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

Where

P=\left ( 1-\frac{1}{x} \right )

I.F=e^{\int P\, dx}=e^{\int(1-\frac{1}{x}) dx}=e^{(x-in\, x)}

I.F=e^{x}.e^{-in\, x}=e^{x}.e^{in_{e}\, (x^{-1})}=e^{x}.\frac{1}{x}=\frac{e^{x}}{x}

So, the answer is

\frac{e^{x}}{x}

Posted by

Gurleen Kaur

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