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  • Explain solution RD Sharma class 12 chapter Differential Equation exercise 21.2 question 15.3 subquestion (iii) maths

Explain solution RD Sharma class 12 chapter Differential Equation exercise 21.2 question 15.3 subquestion (iii) maths

Answers (1)

Answer:

 4xy\frac{\mathrm{d} y}{\mathrm{d} x}+x^{2}-2y^{2}=0

Hint:

 Using the formula (a+b)2 and differentiating the given equation

Given:

 (x-a)^{2}+2y^{2}=a^{2}

Solution:

\begin{aligned} &2(x-a)+2y.2\frac{\mathrm{d} y}{\mathrm{d} x}=0\\ &(x-a)=-2y\frac{\mathrm{d} y}{\mathrm{d} x}\\ &a=x+2y\frac{\mathrm{d} y}{\mathrm{d} x}\\ &\left ( 2+\frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}+2y^{2}=x^{2}+\left ( 2+\frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}+2x.2y\frac{\mathrm{d} y}{\mathrm{d} x} \end{aligned}

4xy\frac{\mathrm{d} y}{\mathrm{d} x}+x^{2}-2y^{2}=0

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Gurleen Kaur

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