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  • Please solve RD Sharma class 12 chapter Differential Equation exercise 21.3 question 13 maths textbook solution

Please solve RD Sharma class 12 chapter Differential Equation exercise 21.3 question 13 maths textbook solution

Answers (1)

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Answer:

y=c x+2 c^{2}  is a solution of differential equation

Hint:

Just differentiate once and put value in given differential problem

Given:

y=c x+2 c^{2}  is a solution of the equation


Solution:

Differentiating on both sides with respect to x

\begin{aligned} &\frac{d y}{d x}=\frac{d(c x)}{d x}+\frac{d\left(2 c^{2}\right)}{d x} \\\\ &\frac{d y}{d x}=c \end{aligned}                    ................(i)

Put value in given problem as follows

\begin{aligned} &2\left(\frac{d y}{d x}\right)^{2}+x \frac{d y}{d x}-y=0 \\\\ &L H S=2\left(\frac{d y}{d x}\right)^{2}+x \frac{d y}{d x}-y \end{aligned}

\begin{aligned} &=2 c^{2}+x c-y \\\\ &=2 c^{2}+x c-\left(c x+2 c^{2}\right) \\\\ &=2 c^{2}+x c-c x-2 c^{2} \\\\ &=0 \\\\ &=R H S \end{aligned}

Thus, y=c x+2 c^{2}  is a solution of differential equation.

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