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UPSEE Solved Model Paper 4

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Question : 129 of 150

Marks: +1, -0

The solution of dy/dx = y/x + tan (y/x).

sin (y/x) = cx
sin (y/x) = cy
cos (y/x) = cx
sec (y/x) + tan (y/x) = xc

Solution:

\frac{dy}{dx}

=

\frac{g}{n} + \tan\left(\frac{y}{x}\right)

It is homogeneous differential equation

Let y =

\sqrt{x}

⇒

\frac{dy}{dx}

=

\sqrt{+\frac{x dv}{dx}}

and put in differential equation

⇒

\sqrt{+ x \frac{dv}{dx}}

=

\sqrt{+\tan v}

⇒

\frac{x dv}{dx}

= tan v

⇒ ∫

\frac{dv}{\tan v}

= ∫

\frac{dx}{x}

⇒ ∫ sec v = log x + c

⇒ log |sec v = tan v| log xc

⇒ log

\left|\sec\frac{y}{x} + \tan\frac{y}{x}\right|

= log xc

\left|\sec\frac{y}{x} + \tan\frac{y}{x}\right|

= xc

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