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

Answers (1)

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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