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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.

  Is there an error in this question or solution?
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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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