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  • Explain solution RD Sharma class 12 chapter 21 Differential Equation exercise Fill in the blank question 12 maths

Explain solution RD Sharma class 12 chapter 21 Differential Equation exercise Fill in the blank question 12 maths

Answers (1)

Answer:

 \frac{1}{x}

Hint:

 Using the form of linear differential equation

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

Given:

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

Solution:

x\frac{\mathrm{d} y}{\mathrm{d} x}-y=x\, cos\, x \qquad \qquad \dots(i)

Divide the eqn (i) by x, we get

\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{y}{x}= cos\, x \qquad \qquad \dots(ii)

Comparing eqn (ii) with the standard linear differential equation

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

We get,

P=-\frac{1}{x}, \quad Q=cos \, x

\therefore I.F=e^{\int P\, dx}=e^{\int\frac{-1}{x} dx}=e^{-log\, x}

I.F=e^{log\, x^{-1}}=\frac{1}{x}

∴So the answer is

\frac{1}{x}

Posted by

Gurleen Kaur

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