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

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 Using the form of linear differential equation

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


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


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


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Gurleen Kaur

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