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# In the Following Verify that the Given Functions (Explicit Or Implicit) is a Solution of the Corresponding Differential Equation:- Y = X Sin X X Y ' = Y + X √ X 2 − Y 2 - Mathematics

Sum

In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

y = x sin x              xy'=y+xsqrt(x^2-y^2)

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#### Solution

We have,

xy'=y+xsqrt(x^2-y^2)  ................(1)

Now,

y = x sin x

rArry'=sinx + xcosx

Putting the above value in (1), we get

LHS = x (sin x + x cos x)

= x sin x + x2 cos x

= x sin x + x(x cos x)

=xsinx+x(xsqrt(1-sin^2x))

=xsinx+x(x^2-x^2sin^2x)

=y+x(sqrt(x^2-y^2)="RHS"

Thus, y= x sin x is the solution of the given differential equation.

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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 22 Differential Equations
Revision Exercise | Q 3.5 | Page 144
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