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  • Please solve RD Sharma class 12 chapter Differential Equation exercise 21.3 question 21 sub question (v) maths textbook solution

Please solve RD Sharma class 12 chapter Differential Equation exercise 21.3 question 21 sub question (v) maths textbook solution

Answers (1)

best_answer

Answer:

y=\frac{1}{4}(x \pm a)^{2}   is a solution of differential equation

Hint:

Differentiate the function

Given:

y=\frac{1}{4}(x \pm a)^{2}

Solution:

Differentiating on both sides with respect to x

\begin{aligned} &\frac{d y}{d x}=\frac{1}{4} \times 2(x \pm a)(1) \\\\ &\frac{d y}{d x}=\frac{1}{2}(x \pm a) \end{aligned}                    ..............(i)

Squaring on both sides,

\begin{aligned} &\left(\frac{d y}{d x}\right)^{2}=\frac{1}{4}(x \pm a)^{2} \\\\ &\left(\frac{d y}{d x}\right)^{2}=y \\\\ &y=\left(\frac{d y}{d x}\right)^{2} \end{aligned}

Hence, the given function satisfies the equation.

 

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