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  • Please solve RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 28 maths textbook solution.

Please solve RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 28 maths textbook solution.

Answers (1)

Answer : \text { (d) } x^{3}+y^{3}=12 x+C

Hint: Use Variable separable form i.e. separate y and x terms by taking x terms to one side and y terms to the other.

Given:   x^{2}+y^{2} \frac{d y}{d x}=4

Explanation : y^{2} \frac{d y}{d x}=4-x^{2}

\Rightarrow y^{2} d y=d x\left(4-x^{2}\right)

Integrate both sides

\begin{aligned} &\Rightarrow \frac{y^{3}}{3}=4 x-\frac{x^{3}}{3}+C_{1} \\ &\Rightarrow y^{3}=3(4 x)-3\left(\frac{x^{3}}{3}\right)+3 C_{1} \end{aligned}

\begin{aligned} &\Rightarrow y^{3}=12 x-x^{3}+3 C_{1} \\ &\Rightarrow x^{3}+y^{3}=12 x+3 C_{1} \\ &\Rightarrow x^{3}+y^{3}=12 x+C\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \quad\left[C=3 C_{1}\right] \end{aligned}

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