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Provide solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise 21.10 Question 7 textbook solution.    

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Answer : y=\left(\frac{x-1}{x}\right) e^{x}+\frac{c}{x}

Hint: To solve this equation we will use differentiate different.

Give : x\frac{dy}{dx}+y=xe^{x}

Solution : \frac{dy}{dx}+Py=Q

                \begin{aligned} &P=\frac{1}{x^{\prime}} Q=e^{x} \\ \end{aligned}

               \begin{aligned} &I f=e^{\int P d x} \\ \end{aligned}

                     \begin{aligned} &=e^{\int \frac{1}{x} d x} \\ \end{aligned}

                     \begin{aligned} &=e^{\log e^{x}} \\ \end{aligned}

                     \begin{aligned} &=x \end{aligned}

                \begin{aligned} &\\ &y x=\int e^{x} xdx\\ &y x=x e^{x}+\int e^{x}+C \end{aligned}

                \begin{aligned} &y x=(x+1) e^{x}+C \\ \end{aligned}

               \begin{aligned} &y=y \frac{(x-1)}{x} e^{x}+\frac{C}{x} \end{aligned}


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