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Explain solution RD Sharma class 12 chapter 21 Differential Equation exercise Fill in the blank question 8 maths

Answers (1)

Answer:

 \frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}+y=0

Hint:

 Differentiating the given function w.r.t ‘x’

Given:

 y=Asin\, x+Bcos\, x

Solution:

Differentiating the given function w.r.t ‘x’ we get,

\frac{\mathrm{d} y}{\mathrm{d} x}=Acos\, x-Bsin\, x

and

\frac{\mathrm{d}^{2} y}{\mathrm{d} x^{2}}=-Asin\, x-Bcos\, x

\Rightarrow \frac{\mathrm{d}^{2} y}{\mathrm{d} x^{2}}+y=0

is the required differential equation.

∴So, the answer is

\frac{\mathrm{d}^{2} y}{\mathrm{d} x^{2}}+y=0

Posted by

Gurleen Kaur

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