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  • Please solve RD Sharma class 12 chapter Differential Equation exercise 21.2 question 16 subquestion (ix) maths textbook solution

Please solve RD Sharma class 12 chapter Differential Equation exercise 21.2 question 16 subquestion (ix) maths textbook solution

Answers (1)

Answer:

 The required equation is

2xy\frac{\mathrm{d} y}{\mathrm{d} x}=(x^{2}+3y^{2})

Hint:

 Differentiating the given equation with respect to x

Given:

 x^{2}+y^{2}=ax^{3}

Solution:

\begin{aligned} &x^{2}+y^{2}=ax^{3} \\ &a=\frac{x^{2}+y^{2}}{x^{3}} \end{aligned}

Differentiating with respect to x,

\begin{aligned} &\frac{\left [ \left ( 2x+2y\frac{\mathrm{d} y}{\mathrm{d} x} \right )x^{3}-3x^{2}(x^{2}+y^{2}) \right ]}{x^{6}}=0 \\ &2x^{4}+2x^{3}y\frac{\mathrm{d} y}{\mathrm{d} x}-3x^{4}-3x^{2}y^{2}=0 \\ &2x^{3}y\frac{\mathrm{d} y}{\mathrm{d} x}-x^{4}-3x^{2}y^{2}=0 \end{aligned}

\begin{aligned} &2x^{3}y\frac{\mathrm{d} y}{\mathrm{d} x}=x^{4}+3x^{2}y^{2} \\ &2x^{3}y\frac{\mathrm{d} y}{\mathrm{d} x}=x^{2}(x^{2}+3y^{2}) \\ &2xy\frac{\mathrm{d} y}{\mathrm{d} x}=(x^{2}+3y^{2}) \end{aligned}

 The required equation is

2xy\frac{\mathrm{d} y}{\mathrm{d} x}=(x^{2}+3y^{2})

Posted by

Gurleen Kaur

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