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  • Please solve RD Sharma class 12 chapter Differential Equations exercise 21.11 question 21 maths textbook solution

Please solve RD Sharma class 12 chapter Differential Equations exercise 21.11 question 21 maths textbook solution

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Answer: 9 y+4 x^{2}=0

Given: Curve passes through \left ( 3,-4 \right ) and given slope of curve =\frac{2y}{x}

To find: We have to show that the equation which satisfies the curve.

Hint: Solve of curve =\frac{2 y}{x}, \frac{d y}{d x}=\frac{2 y}{x}, solve this to find the equation of the curve.

Solution: Slope of curve =\frac{2 y}{x}

        \begin{aligned} &=\frac{d y}{d x}=\frac{2 y}{x} \\\\ &=\frac{d y}{y}=\frac{2}{x} d x \end{aligned}

Integrating on both sides

        \begin{aligned} &=\int \frac{d y}{y}=2 \int \frac{d x}{x} \\\\ &=\log y=2 \log x+\log C \\\\ &=y=x^{2} C \ldots(i) \end{aligned}

As it passes through \left ( 3,-4 \right )

        \begin{aligned} &=-4=(3)^{2} C \\\\ &=-4=9 C \\\\ &=C=-\frac{4}{9} \end{aligned}

So equation (i) becomes

        \begin{aligned} &=y=-\frac{4}{9} x^{2} \\\\ &=9 y=-4 x^{2} \\\\ &=9 y+4 x^{2}=0 \end{aligned}

 

 

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