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  • Explain solution RD Sharma class 12 chapter Differential Equation exercise 21.3 question 21 sub question (iv) maths

Explain solution RD Sharma class 12 chapter Differential Equation exercise 21.3 question 21 sub question (iv) maths

Answers (1)

Answer:

y=a x+b+\frac{1}{2 x}   is a solution of differential equation

Hint:

Differentiate the function.

Given:

y=a x+b+\frac{1}{2 x}  


Solution:

Differentiating on both sides with respect to x

\begin{aligned} &\frac{d y}{d x}=a+\frac{1}{2}\left(\frac{-1}{x^{2}}\right) \\\\ &\frac{d y}{d x}=a-\frac{1}{2 x^{2}} \end{aligned}                .................(i)

Differentiating equation (i)

\begin{aligned} &\frac{d^{2} y}{d x^{2}}=\frac{-1}{2}\left(\frac{-2}{x^{3}}\right) \\\\ &\frac{d^{2} y}{d x^{2}}=\frac{1}{x^{3}} \\\\ &x^{3} \frac{d^{2} y}{d x^{2}}=1 \end{aligned}

Hence the given function is the solution of differential equation.

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