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Explain solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Revision Exercise (RE) Question 66 Subquestion (viii) textbook solution.

Answers (1)

Answer : x y=\frac{x^{4}}{4}+c

Hint : : integrate by applying integration of  y^{n}

Given : \frac{d y}{d x}+\frac{y}{x}=x^{2}

Solution : \frac{d y}{d x}+\frac{y}{x}=x^{2}

Differential equation is in the form of

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

P=\frac{1}{x}                        , Q=x^{2}

Putting I.F

\begin{aligned} &\text { I.F }=e^{\int P d x} \\ &\text { I.F }=e^{\int \frac{1}{x} d x} \\ &\text { I.F }=e^{\log x} \\ &\text { I.F }=x \end{aligned}

Solution is

\begin{aligned} &y \times I . F=\int(Q \times I . F) d x+c \\ &y x=\int x^{2} \times x d x+c \\ &y x=\int x^{3} d x+c \\ &y x=\frac{x^{4}}{4}+c \end{aligned}


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