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  • Explain solution RD Sharma class 12 chapter Differential Equation exercise 21.2 question 13 maths

Explain solution RD Sharma class 12 chapter Differential Equation exercise 21.2 question 13 maths

Answers (1)

Answer:

 \frac{\mathrm{d} y}{\mathrm{d} x}+2xy=4x^{3}

Hint:

 \begin{aligned} &y=2(x^{2}-1)+ce^{-x^{2}} \\ &y=2x^{2}-2+ce^{-x^{2}} \\ &2x^{2}-y=2-ce^{-x^{2}} \\ &\text { Substitutes } 2-ce^{-x^{2}} \text { by } 2x^{2}-y \end{aligned}

Given:

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

Hence proved.

Posted by

Gurleen Kaur

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