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Please solve RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Revision Exercise (RE) Question 66 Subquestion (xv) textbook solution.

Answers (1)

Answer : x=3 y^{2}+c y

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

Given  : \left(x+3 y^{2}\right) \frac{d y}{d x}=y

Solution : \left(x+3 y^{2}\right) \frac{d y}{d x}=y

This is not in the foem of \frac{d x}{d y}+Px=Q

Where P_{1}=\frac{-1}{y} \& Q=3 y

Step : 3  find integration factor

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

Step : 4

Solution is

\begin{aligned} x(I . F) &=\int Q \times I . F d y+c \\ x \frac{1}{y} &=\int 3 y \frac{1}{y} d y+c \\ \frac{x}{y} &=3 \int d y+c \end{aligned}

          \begin{array}{r} \frac{x}{y}=3 y+c \\ \end{array}

\begin{array}{r} x=3 y^{2}+c y \end{array}

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