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Please solve RD Sharma class 12 chapter 21 Differential Equation exercise Fill in the blank question 5 maths textbook solution

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 We will use the method of solving linear differential equation.


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


The given differential equation can be written as

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

The given differential equation is of the form

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

and therefore by comparison we get;

P=\frac{-1}{x}, \qquad Q=\frac{sin\, x}{x}

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

So, the answer is


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Gurleen Kaur

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